GPT-4o on 3.MD.D.8-polygon
Common Core Standard 3.MD.D.8-polygon
This standard covers the following:
Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
Problem: A sum of several measurements taken along the edge of a plot of land totals to 368 miles. The individual measurements are 41 miles, 28 miles, 90 miles, 32 miles, 10 miles, and 98 miles. What is the remaining measurement that hasn't been included in the total yet?
GPT-4o:
To find the remaining measurement, we first sum the given individual measurements: \[ 41 + 28 + 90 + 32 + 10 + 98 \] Let's add these step-by-step: \[ 41 + 28 = 69 \] \[ 69 + 90 = 159 \] \[ 159 + 32 = 191 \] \[ 191 + 10 = 201 \] \[ 201 + 98 = 299 \] The total of the given measurements is 299 miles. The total measurement of the plot of land is 368 miles. To find the remaining measurement, we subtract the sum of the given measurements from the total: \[ 368 - 299 = 69 \] ### Answer: 69 miles
Expected answer: 69
Correct? Yes
Problem: A regular pentagon has side lengths of 70cm, 36cm, 53cm, and 45cm. If the total perimeter of the pentagon is 300cm, what is the length of its fifth side?
GPT-4o:
To find the length of the fifth side of the regular pentagon, we first need to sum the lengths of the four given sides and then subtract this sum from the total perimeter. The given side lengths are: - 70 cm - 36 cm - 53 cm - 45 cm First, we sum these lengths: \[ 70 + 36 + 53 + 45 \] Calculating step-by-step: \[ 70 + 36 = 106 \] \[ 106 + 53 = 159 \] \[ 159 + 45 = 204 \] The total perimeter of the pentagon is 300 cm. To find the length of the fifth side, we subtract the sum of the four given sides from the total perimeter: \[ 300 - 204 = 96 \] ### Answer: 96 cm
Expected answer: 96
Correct? Yes
Problem: A regular nonagon (9-sided polygon) has side lengths of 14cm, 94cm, 3cm, 20cm, 57cm, 83cm, 96cm, and 85cm. If the perimeter of the nonagon is 521cm, what is the length of the ninth side?
GPT-4o:
To find the length of the ninth side of the nonagon, we first need to sum the lengths of the given eight sides and then subtract this sum from the total perimeter. The given side lengths are: 14 cm, 94 cm, 3 cm, 20 cm, 57 cm, 83 cm, 96 cm, and 85 cm. First, we sum these lengths: \[ 14 + 94 + 3 + 20 + 57 + 83 + 96 + 85 \] Let's add them step by step: \[ 14 + 94 = 108 \] \[ 108 + 3 = 111 \] \[ 111 + 20 = 131 \] \[ 131 + 57 = 188 \] \[ 188 + 83 = 271 \] \[ 271 + 96 = 367 \] \[ 367 + 85 = 452 \] The sum of the given eight sides is 452 cm. The total perimeter of the nonagon is 521 cm. To find the length of the ninth side, we subtract the sum of the eight sides from the total perimeter: \[ 521 - 452 = 69 \] ### Answer: 69 cm
Expected answer: 69
Correct? Yes
Problem: A polygon has sides measuring 54cm, 51cm, 5cm, 22cm, and 93cm. If the total perimeter of the polygon is 274cm, what is the length of the sixth side?
GPT-4o:
To find the length of the sixth side of the polygon, we need to subtract the sum of the known side lengths from the total perimeter.
First, let's add the lengths of the known sides:
\[ 54 \, \text{cm} + 51 \, \text{cm} + 5 \, \text{cm} + 22 \, \text{cm} + 93 \, \text{cm} \]
Calculating the sum step-by-step:
\[ 54 + 51 = 105 \]
\[ 105 + 5 = 110 \]
\[ 110 + 22 = 132 \]
\[ 132 + 93 = 225 \]
The sum of the known side lengths is 225 cm.
Next, we subtract this sum from the total perimeter to find the length of the sixth side:
\[ 274 \, \text{cm} - 225 \, \text{cm} = 49 \, \text{cm} \]
### Answer: 49 cm
Expected answer: 49
Correct? Yes
Problem: A regular pentagon has a perimeter of 310 m. What is the length of each side?
GPT-4o:
To find the length of each side of a regular pentagon, we need to divide the perimeter by the number of sides. A regular pentagon has 5 sides.
Given the perimeter is 310 meters, we calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{310 \, \text{m}}{5}
\]
\[
\text{Length of each side} = 62 \, \text{m}
\]
### Answer: 62 m
Expected answer: 62
Correct? Yes
Problem: A polygon has side lengths of 78cm, 93cm, 21cm, 4cm, and 21cm. If the total perimeter of the shape is 315cm, then what is the length of the last side?
GPT-4o:
To find the length of the last side of the polygon, we need to sum the given side lengths and subtract this sum from the total perimeter.
First, let's sum the given side lengths:
\[ 78 \, \text{cm} + 93 \, \text{cm} + 21 \, \text{cm} + 4 \, \text{cm} + 21 \, \text{cm} \]
Calculating step-by-step:
\[ 78 + 93 = 171 \]
\[ 171 + 21 = 192 \]
\[ 192 + 4 = 196 \]
\[ 196 + 21 = 217 \]
The sum of the given side lengths is 217 cm.
Next, we subtract this sum from the total perimeter to find the length of the last side:
\[ 315 \, \text{cm} - 217 \, \text{cm} = 98 \, \text{cm} \]
### Answer: 98 cm
Expected answer: 98
Correct? Yes
Problem: A regular 8-sided polygon, an octagon, has a perimeter of 160m. What is the length of each side?
GPT-4o:
To find the length of each side of a regular 8-sided polygon (octagon), we need to divide the total perimeter by the number of sides.
Given:
- Perimeter of the octagon = 160 meters
- Number of sides = 8
The length of each side is calculated as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{160 \text{ meters}}{8}
\]
Performing the division:
\[
\frac{160}{8} = 20 \text{ meters}
\]
### Answer: 20 meters
Expected answer: 20
Correct? Yes
Problem: Consider an octagon. Its seven sides have lengths 6cm, 4cm, 95cm, 34cm, 19cm, 14cm, and 26cm. What is the length of the other side if the total perimeter of the octagon is 224cm?
GPT-4o:
To find the length of the missing side of the octagon, we first need to sum the lengths of the seven given sides and then subtract this sum from the total perimeter. The given side lengths are: 6 cm, 4 cm, 95 cm, 34 cm, 19 cm, 14 cm, and 26 cm. First, we sum these lengths: \[ 6 + 4 + 95 + 34 + 19 + 14 + 26 \] Let's add them step by step: \[ 6 + 4 = 10 \] \[ 10 + 95 = 105 \] \[ 105 + 34 = 139 \] \[ 139 + 19 = 158 \] \[ 158 + 14 = 172 \] \[ 172 + 26 = 198 \] The sum of the seven given sides is 198 cm. The total perimeter of the octagon is 224 cm. To find the length of the missing side, we subtract the sum of the given sides from the total perimeter: \[ 224 - 198 = 26 \] ### Answer: 26 cm
Expected answer: 26
Correct? Yes
Problem: A regular hexagon has a perimeter of 174 meters. If all sides are equal, what is the length of one side?
GPT-4o:
To find the length of one side of a regular hexagon, we need to divide the perimeter by the number of sides. A regular hexagon has 6 equal sides.
Given the perimeter is 174 meters, we calculate the length of one side as follows:
\[
\text{Length of one side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{174 \text{ meters}}{6}
\]
\[
\text{Length of one side} = 29 \text{ meters}
\]
### Answer: 29 meters
Expected answer: 29
Correct? Yes
Problem: A dodecagon has side lengths of 65cm, 22cm, 32cm, 31cm, 78cm, 88cm, 7cm, 29cm, 36cm, and 54cm. The total perimeter of the dodecagon is 538cm. What is the length of the 11th side?
GPT-4o:
To find the length of the 11th side of the dodecagon, we need to sum the lengths of the given sides and subtract this sum from the total perimeter. First, let's sum the lengths of the given sides: \[ 65 + 22 + 32 + 31 + 78 + 88 + 7 + 29 + 36 + 54 \] Calculating step-by-step: \[ 65 + 22 = 87 \] \[ 87 + 32 = 119 \] \[ 119 + 31 = 150 \] \[ 150 + 78 = 228 \] \[ 228 + 88 = 316 \] \[ 316 + 7 = 323 \] \[ 323 + 29 = 352 \] \[ 352 + 36 = 388 \] \[ 388 + 54 = 442 \] The sum of the given side lengths is 442 cm. The total perimeter of the dodecagon is 538 cm. To find the length of the 11th side, we subtract the sum of the given sides from the total perimeter: \[ 538 - 442 = 96 \] ### Answer: 96 cm
Expected answer: 96
Correct? Yes
Problem: A hexagon has five side lengths of 61 cm, 84 cm, 80 cm, 11 cm, and 71 cm. What should be the length of the last side so that the sum of lengths of all sides is 357 cm?
GPT-4o:
To find the length of the last side of the hexagon, we first need to sum the lengths of the five given sides:
\[ 61 \, \text{cm} + 84 \, \text{cm} + 80 \, \text{cm} + 11 \, \text{cm} + 71 \, \text{cm} \]
Let's calculate this step-by-step:
\[ 61 + 84 = 145 \]
\[ 145 + 80 = 225 \]
\[ 225 + 11 = 236 \]
\[ 236 + 71 = 307 \]
The sum of the five given sides is 307 cm. The total length of all six sides should be 357 cm. Therefore, the length of the last side is:
\[ 357 \, \text{cm} - 307 \, \text{cm} = 50 \, \text{cm} \]
### Answer: 50 cm
Expected answer: 50
Correct? Yes
Problem: A regular octagon has a perimeter of 544m. What is the length of one side?
GPT-4o:
To find the length of one side of a regular octagon, we need to divide the perimeter by the number of sides. A regular octagon has 8 sides.
Given:
Perimeter of the octagon = 544 meters
We calculate the length of one side as follows:
\[
\text{Length of one side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{544 \, \text{m}}{8}
\]
Performing the division:
\[
\frac{544}{8} = 68 \, \text{m}
\]
### Answer: 68 meters
Expected answer: 68
Correct? Yes
Problem: The perimeter of a regular decagon (10-sided polygon) is 960m. Find the length of one side.
GPT-4o:
To find the length of one side of a regular decagon, we need to divide the perimeter by the number of sides.
The perimeter of the decagon is 960 meters, and a decagon has 10 sides.
So, the length of one side is:
\[ \text{Length of one side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{960 \, \text{m}}{10} = 96 \, \text{m} \]
### Answer: 96 m
Expected answer: 96
Correct? Yes
Problem: A regular heptagon (7-sided polygon) has an unknown side length. If its total perimeter is 203m, how long is each side?
GPT-4o:
To find the side length of a regular heptagon, we need to divide the total perimeter by the number of sides.
A heptagon has 7 sides. Given that the total perimeter is 203 meters, we can set up the following equation to find the side length \( s \):
\[ s = \frac{\text{Total Perimeter}}{\text{Number of Sides}} \]
Substituting the given values:
\[ s = \frac{203 \, \text{m}}{7} \]
Now, perform the division:
\[ s = 29 \, \text{m} \]
### Answer: 29 m
Expected answer: 29
Correct? Yes
Problem: A regular heptagon (7-sided polygon) has a perimeter of 49 meters. What is the length of each side?
GPT-4o:
To find the length of each side of a regular heptagon, we need to divide the perimeter by the number of sides.
Given:
- Perimeter of the heptagon = 49 meters
- Number of sides in a heptagon = 7
We calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{49 \text{ meters}}{7}
\]
Performing the division:
\[
\frac{49}{7} = 7 \text{ meters}
\]
### Answer: 7 meters
Expected answer: 7
Correct? Yes
Problem: The perimeter of a regular heptagon is 329m. What is the length of each side?
GPT-4o:
To find the length of each side of a regular heptagon, we need to divide the perimeter by the number of sides. A heptagon has 7 sides.
Given:
- Perimeter of the heptagon = 329 meters
- Number of sides = 7
We calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{329 \, \text{m}}{7}
\]
Performing the division:
\[
\frac{329}{7} = 47 \, \text{m}
\]
### Answer: 47 meters
Expected answer: 47
Correct? Yes
Problem: The sides of a heptagon have lengths of 86m, 80m, 47m, 93m, and 99m. If the total perimeter of the heptagon is 486m, what is the length of the sixth side?
GPT-4o:
To find the length of the sixth side of the heptagon, we first need to sum the lengths of the five given sides and then subtract this sum from the total perimeter. The given side lengths are: - 86 meters - 80 meters - 47 meters - 93 meters - 99 meters First, we add these lengths together: \[ 86 + 80 + 47 + 93 + 99 \] Let's perform the addition step-by-step: \[ 86 + 80 = 166 \] \[ 166 + 47 = 213 \] \[ 213 + 93 = 306 \] \[ 306 + 99 = 405 \] The sum of the given side lengths is 405 meters. The total perimeter of the heptagon is 486 meters. To find the length of the sixth side, we subtract the sum of the given side lengths from the total perimeter: \[ 486 - 405 = 81 \] ### Answer: 81 meters
Expected answer: 81
Correct? Yes
Problem: A regular heptagon has a perimeter of 546m. What is the length of each side?
GPT-4o:
To find the length of each side of a regular heptagon, we need to divide the perimeter by the number of sides. A heptagon has 7 sides.
Given:
- Perimeter of the heptagon = 546 meters
- Number of sides = 7
We calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{546 \text{ meters}}{7}
\]
Performing the division:
\[
\frac{546}{7} = 78
\]
So, the length of each side of the heptagon is 78 meters.
### Answer: 78 meters
Expected answer: 78
Correct? Yes
Problem: A nonagon (nine-sided polygon) has 8 of its sides with lengths 26cm, 45cm, 75cm, 68cm, 63cm, 80cm, and 100cm, respectively. If the perimeter of the nonagon is 532cm, what is the length of the ninth side?
GPT-4o:
To find the length of the ninth side of the nonagon, we first need to sum the lengths of the given 8 sides and then subtract this sum from the total perimeter. The given side lengths are: 26 cm, 45 cm, 75 cm, 68 cm, 63 cm, 80 cm, 100 cm, and 75 cm. First, we sum these lengths: \[ 26 + 45 + 75 + 68 + 63 + 80 + 100 + 75 \] Let's add them step by step: \[ 26 + 45 = 71 \] \[ 71 + 75 = 146 \] \[ 146 + 68 = 214 \] \[ 214 + 63 = 277 \] \[ 277 + 80 = 357 \] \[ 357 + 100 = 457 \] \[ 457 + 75 = 532 \] The total sum of the 8 sides is 532 cm. Given that the perimeter of the nonagon is 532 cm, we subtract the sum of the 8 sides from the total perimeter to find the length of the ninth side: \[ 532 - 532 = 0 \] ### Answer: 0 cm
Expected answer: 75
Correct? No
Problem: The sides of a decagon are 62m, 76m, 98m, 74m, another unknown side, 54m, 4m, 24m, and 48m respectively. All sides are equal in length. If the perimeter of the shape is 452m, what is the length of the unknown side?
GPT-4o:
To find the length of the unknown side, we first need to determine the total length of the known sides and then subtract this from the total perimeter. The known sides of the decagon are: 62m, 76m, 98m, 74m, 54m, 4m, 24m, and 48m. First, we sum these known sides: \[ 62 + 76 + 98 + 74 + 54 + 4 + 24 + 48 \] Let's calculate this step-by-step: \[ 62 + 76 = 138 \] \[ 138 + 98 = 236 \] \[ 236 + 74 = 310 \] \[ 310 + 54 = 364 \] \[ 364 + 4 = 368 \] \[ 368 + 24 = 392 \] \[ 392 + 48 = 440 \] The total length of the known sides is 440 meters. The perimeter of the decagon is given as 452 meters. To find the length of the unknown side, we subtract the total length of the known sides from the perimeter: \[ 452 - 440 = 12 \] ### Answer: 12 meters
Expected answer: 12
Correct? Yes
Problem: A regular hexagon has a perimeter of 78m. What is the length of each side?
GPT-4o:
To find the length of each side of a regular hexagon, we need to remember that a regular hexagon has six equal sides.
Given the perimeter of the hexagon is 78 meters, we can set up the following equation to find the length of one side:
\[ \text{Perimeter} = 6 \times \text{side length} \]
Substituting the given perimeter:
\[ 78 = 6 \times \text{side length} \]
To find the side length, we divide both sides of the equation by 6:
\[ \text{side length} = \frac{78}{6} \]
\[ \text{side length} = 13 \]
### Answer: 13 meters
Expected answer: 13
Correct? Yes
Problem: A regular nonagon has a perimeter of 171m. What is the length of each side?
GPT-4o:
To find the length of each side of a regular nonagon, we need to divide the perimeter by the number of sides. A nonagon has 9 sides.
Given:
- Perimeter of the nonagon = 171 meters
- Number of sides = 9
We calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{171 \, \text{m}}{9}
\]
Performing the division:
\[
\frac{171}{9} = 19 \, \text{m}
\]
### Answer: 19 meters
Expected answer: 19
Correct? Yes
Problem: A nonagon has the following side lengths: 8 cm, 17 cm, 30 cm, 17 cm, 86 cm, 55cm, and 68cm. It also has one unknown side length. The overall perimeter of the nonagon is 318 cm. What is the length of the unknown side?
GPT-4o:
To find the length of the unknown side, we first need to sum the known side lengths of the nonagon and then subtract this sum from the total perimeter. The known side lengths are: 8 cm, 17 cm, 30 cm, 17 cm, 86 cm, 55 cm, and 68 cm. First, we sum these known side lengths: \[ 8 + 17 + 30 + 17 + 86 + 55 + 68 \] Let's add them step by step: \[ 8 + 17 = 25 \] \[ 25 + 30 = 55 \] \[ 55 + 17 = 72 \] \[ 72 + 86 = 158 \] \[ 158 + 55 = 213 \] \[ 213 + 68 = 281 \] The sum of the known side lengths is 281 cm. The total perimeter of the nonagon is 318 cm. To find the unknown side length, we subtract the sum of the known side lengths from the total perimeter: \[ 318 - 281 = 37 \] ### Answer: 37 cm
Expected answer: 37
Correct? Yes
Problem: An 11-sided regular polygon has a perimeter of 858m. What is the length of each side?
GPT-4o:
To find the length of each side of an 11-sided regular polygon with a perimeter of 858 meters, we need to divide the total perimeter by the number of sides.
First, we note that the polygon has 11 sides.
Next, we divide the perimeter by the number of sides:
\[ \text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} \]
Substituting the given values:
\[ \text{Length of each side} = \frac{858 \, \text{m}}{11} \]
Performing the division:
\[ \text{Length of each side} = 78 \, \text{m} \]
### Answer: 78 m
Expected answer: 78
Correct? Yes
Problem: A regular decagon has a perimeter of 360m. What is the length of each side?
GPT-4o:
To find the length of each side of a regular decagon, we need to divide the perimeter by the number of sides. A regular decagon has 10 sides.
Given:
- Perimeter of the decagon = 360 meters
- Number of sides = 10
We calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{360 \text{ meters}}{10} = 36 \text{ meters}
\]
### Answer: 36 meters
Expected answer: 36
Correct? Yes
Problem: A regular hexagon has a perimeter of 522m. What is the length of each side?
GPT-4o:
To find the length of each side of a regular hexagon, we need to remember that a regular hexagon has six equal sides.
Given the perimeter of the hexagon is 522 meters, we can set up the following equation:
\[ \text{Perimeter} = 6 \times \text{side length} \]
Let \( s \) be the length of each side. Then:
\[ 6s = 522 \]
To find \( s \), we divide both sides of the equation by 6:
\[ s = \frac{522}{6} \]
\[ s = 87 \]
### Answer: 87 meters
Expected answer: 87
Correct? Yes
Problem: A regular polygon has a perimeter of 418m. If each side is the same length, what is the length of each side? Assume the polygon has 11 sides.
GPT-4o:
To find the length of each side of a regular polygon, we divide the perimeter by the number of sides.
Given:
- Perimeter of the polygon = 418 meters
- Number of sides = 11
We use the formula for the length of each side:
\[ \text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} \]
Substituting the given values:
\[ \text{Length of each side} = \frac{418 \, \text{m}}{11} \]
Performing the division:
\[ \text{Length of each side} = 38 \, \text{m} \]
### Answer: 38 meters
Expected answer: 38
Correct? Yes
Problem: A polygon has side lengths of 56m, 73m, 39m, 24m, and 26m. If the total perimeter of the polygon is 278m, what is the length of the sixth side?
GPT-4o:
To find the length of the sixth side of the polygon, we first need to sum the lengths of the known sides and then subtract this sum from the total perimeter. The known side lengths are: 56m, 73m, 39m, 24m, and 26m. First, we sum these lengths: \[ 56 + 73 + 39 + 24 + 26 \] Let's add them step by step: \[ 56 + 73 = 129 \] \[ 129 + 39 = 168 \] \[ 168 + 24 = 192 \] \[ 192 + 26 = 218 \] The sum of the known side lengths is 218 meters. The total perimeter of the polygon is 278 meters. To find the length of the sixth side, we subtract the sum of the known side lengths from the total perimeter: \[ 278 - 218 = 60 \] ### Answer: 60 meters
Expected answer: 60
Correct? Yes
Problem: A regular pentagon has a perimeter of 385cm. How long is each side?
GPT-4o:
To find the length of each side of a regular pentagon, we need to divide the perimeter by the number of sides. A regular pentagon has 5 sides.
Given:
Perimeter = 385 cm
We calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{385 \, \text{cm}}{5}
\]
Performing the division:
\[
\frac{385}{5} = 77 \, \text{cm}
\]
### Answer: 77 cm
Expected answer: 77
Correct? Yes
Problem: The perimeter of a very irregular eleven-sided polygon is 663m. Of those eleven sides, ten are known to be 97m, 93m, 35m, 1m, 27m, 86m, 68m, 96m, 45m, and 61m respectively. What is the length of the unknown eleventh side?
GPT-4o:
To find the length of the unknown eleventh side, we first need to sum the lengths of the ten known sides and then subtract this sum from the total perimeter. First, let's add the lengths of the ten known sides: \[ 97 + 93 + 35 + 1 + 27 + 86 + 68 + 96 + 45 + 61 \] We can add these step-by-step: \[ 97 + 93 = 190 \] \[ 190 + 35 = 225 \] \[ 225 + 1 = 226 \] \[ 226 + 27 = 253 \] \[ 253 + 86 = 339 \] \[ 339 + 68 = 407 \] \[ 407 + 96 = 503 \] \[ 503 + 45 = 548 \] \[ 548 + 61 = 609 \] The sum of the ten known sides is 609 meters. Next, we subtract this sum from the total perimeter to find the length of the unknown eleventh side: \[ 663 - 609 = 54 \] ### Answer: 54 meters
Expected answer: 54
Correct? Yes
Problem: A decagon has side lengths of 54m, 49m, 85m, 48m, 85m, 19m, 94m, 44m, and 54m respectively. The length of the tenth side is not known. What is the length of this side if the total perimeter of the decagon is 575m?
GPT-4o:
To find the length of the unknown side of the decagon, we first need to sum the known side lengths and then subtract this sum from the total perimeter. The known side lengths are: 54m, 49m, 85m, 48m, 85m, 19m, 94m, 44m, and 54m. First, we sum these known side lengths: \[ 54 + 49 + 85 + 48 + 85 + 19 + 94 + 44 + 54 \] Let's add them step by step: \[ 54 + 49 = 103 \] \[ 103 + 85 = 188 \] \[ 188 + 48 = 236 \] \[ 236 + 85 = 321 \] \[ 321 + 19 = 340 \] \[ 340 + 94 = 434 \] \[ 434 + 44 = 478 \] \[ 478 + 54 = 532 \] The sum of the known side lengths is 532 meters. The total perimeter of the decagon is 575 meters. To find the length of the unknown side, we subtract the sum of the known side lengths from the total perimeter: \[ 575 - 532 = 43 \] ### Answer: 43 meters
Expected answer: 43
Correct? Yes
Problem: Given a regular octagon with a perimeter of 248m, what is the length of each side?
GPT-4o:
To find the length of each side of a regular octagon, we need to divide the perimeter by the number of sides. A regular octagon has 8 sides.
Given:
- Perimeter of the octagon = 248 meters
- Number of sides = 8
We calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{248 \, \text{meters}}{8}
\]
Performing the division:
\[
\frac{248}{8} = 31 \, \text{meters}
\]
### Answer: 31 meters
Expected answer: 31
Correct? Yes
Problem: A regular pentagon has a perimeter of 390m. What is the length of each side?
GPT-4o:
To find the length of each side of a regular pentagon, we need to divide the perimeter by the number of sides. A regular pentagon has 5 sides.
Given:
- Perimeter of the pentagon = 390 meters
- Number of sides = 5
We calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{390 \text{ meters}}{5}
\]
Performing the division:
\[
\frac{390}{5} = 78 \text{ meters}
\]
### Answer: 78 meters
Expected answer: 78
Correct? Yes
Problem: A decagon has nine side lengths given as 6m, 85m, 83m, 73m, 25m, 66m, 54m, 87m, and 21m. If the total perimeter is 522m, find the length of the tenth side.
GPT-4o:
To find the length of the tenth side of the decagon, we first need to sum the given side lengths and then subtract this sum from the total perimeter. The given side lengths are: 6m, 85m, 83m, 73m, 25m, 66m, 54m, 87m, and 21m. First, we sum these side lengths: \[ 6 + 85 + 83 + 73 + 25 + 66 + 54 + 87 + 21 \] Let's add them step by step: \[ 6 + 85 = 91 \] \[ 91 + 83 = 174 \] \[ 174 + 73 = 247 \] \[ 247 + 25 = 272 \] \[ 272 + 66 = 338 \] \[ 338 + 54 = 392 \] \[ 392 + 87 = 479 \] \[ 479 + 21 = 500 \] The sum of the nine given side lengths is 500 meters. The total perimeter of the decagon is 522 meters. To find the length of the tenth side, we subtract the sum of the nine given side lengths from the total perimeter: \[ 522 - 500 = 22 \] ### Answer: 22 meters
Expected answer: 22
Correct? Yes
Problem: A regular octagon has a perimeter of 408m. What is the length of each side?
GPT-4o:
To find the length of each side of a regular octagon, we need to divide the perimeter by the number of sides. A regular octagon has 8 sides.
Given:
Perimeter of the octagon = 408 meters
We calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{408 \text{ meters}}{8}
\]
Performing the division:
\[
\frac{408}{8} = 51 \text{ meters}
\]
### Answer: 51 meters
Expected answer: 51
Correct? Yes
Problem: An octagon has an equal length of sides. If the perimeter of the octagon is 696m, what is the length of each side?
GPT-4o:
To find the length of each side of the octagon, we need to divide the total perimeter by the number of sides. An octagon has 8 sides.
Given:
- Perimeter of the octagon = 696 meters
- Number of sides = 8
We calculate the length of each side as follows:
\[ \text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} \]
\[ \text{Length of each side} = \frac{696 \text{ meters}}{8} \]
\[ \text{Length of each side} = 87 \text{ meters} \]
### Answer: 87 meters
Expected answer: 87
Correct? Yes
Problem: An octagon has a perimeter of 744m. What is the length of each side if all sides are equal?
GPT-4o:
To find the length of each side of the octagon, we need to divide the total perimeter by the number of sides. An octagon has 8 sides.
Given:
- Perimeter of the octagon = 744 meters
- Number of sides = 8
We calculate the length of each side as follows:
\[ \text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} \]
\[ \text{Length of each side} = \frac{744 \, \text{meters}}{8} \]
\[ \text{Length of each side} = 93 \, \text{meters} \]
### Answer: 93 meters
Expected answer: 93
Correct? Yes
Problem: A regular nonagon (9-sided polygon) has a perimeter of 270m. What is the length of one side?
GPT-4o:
To find the length of one side of a regular nonagon, we need to divide the perimeter by the number of sides.
The perimeter of the nonagon is 270 meters, and a nonagon has 9 sides.
So, the length of one side is:
\[ \text{Length of one side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{270 \, \text{m}}{9} \]
Performing the division:
\[ \frac{270}{9} = 30 \, \text{m} \]
### Answer: 30 m
Expected answer: 30
Correct? Yes
Problem: A nonagon nine-sided polygon has eight known side lengths: 30cm, 18cm, 68cm, 23cm, 72cm, 57cm, 33cm, and 19cm. If the total perimeter of the nonagon is 350cm, what is the length of the unknown ninth side?
GPT-4o:
To find the length of the unknown ninth side of the nonagon, we first need to sum the lengths of the eight known sides and then subtract this sum from the total perimeter.
First, let's add the lengths of the eight known sides:
\[ 30 \, \text{cm} + 18 \, \text{cm} + 68 \, \text{cm} + 23 \, \text{cm} + 72 \, \text{cm} + 57 \, \text{cm} + 33 \, \text{cm} + 19 \, \text{cm} \]
Calculating step-by-step:
\[ 30 + 18 = 48 \]
\[ 48 + 68 = 116 \]
\[ 116 + 23 = 139 \]
\[ 139 + 72 = 211 \]
\[ 211 + 57 = 268 \]
\[ 268 + 33 = 301 \]
\[ 301 + 19 = 320 \]
The sum of the eight known side lengths is 320 cm.
Next, we subtract this sum from the total perimeter to find the length of the unknown ninth side:
\[ 350 \, \text{cm} - 320 \, \text{cm} = 30 \, \text{cm} \]
### Answer: 30 cm
Expected answer: 30
Correct? Yes
Problem: A nonagon has eight side lengths known which are 19m, 7m, 10m, 16m, 32m, 15m and 70m. What is the length of the ninth side if the total perimeter of the nonagon is 188m?
GPT-4o:
To find the length of the ninth side of the nonagon, we first need to sum the lengths of the known eight sides and then subtract this sum from the total perimeter. The known side lengths are: 19m, 7m, 10m, 16m, 32m, 15m, 70m, and 19m. First, we sum these lengths: \[ 19 + 7 + 10 + 16 + 32 + 15 + 70 + 19 \] Let's add them step by step: \[ 19 + 7 = 26 \] \[ 26 + 10 = 36 \] \[ 36 + 16 = 52 \] \[ 52 + 32 = 84 \] \[ 84 + 15 = 99 \] \[ 99 + 70 = 169 \] \[ 169 + 19 = 188 \] So, the sum of the known side lengths is 188 meters. Given that the total perimeter of the nonagon is 188 meters, we subtract the sum of the known side lengths from the total perimeter to find the length of the ninth side: \[ 188 - 188 = 0 \] Therefore, the length of the ninth side is: ### Answer: 0 meters.
Expected answer: 19
Correct? No
Problem: A regular hexagon has a perimeter of 90m. What is the length of each side?
GPT-4o:
To find the length of each side of a regular hexagon, we need to remember that a regular hexagon has 6 equal sides.
Given the perimeter of the hexagon is 90 meters, we can set up the following equation:
\[ \text{Perimeter} = 6 \times \text{side length} \]
Let \( s \) be the length of each side. Therefore:
\[ 90 = 6s \]
To find \( s \), we divide both sides of the equation by 6:
\[ s = \frac{90}{6} \]
\[ s = 15 \]
### Answer: 15 meters
Expected answer: 15
Correct? Yes
Problem: A regular heptagon (7-sided polygon) has a perimeter of 287m. What is the length of each side?
GPT-4o:
To find the length of each side of a regular heptagon, we need to divide the perimeter by the number of sides.
The perimeter of the heptagon is 287 meters, and a heptagon has 7 sides.
So, the length of each side is:
\[ \text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{287 \, \text{m}}{7} \]
Performing the division:
\[ \frac{287}{7} = 41 \]
### Answer: 41 meters
Expected answer: 41
Correct? Yes
Problem: A regular pentagon has a perimeter of 50m. What is the length of each side?
GPT-4o:
To find the length of each side of a regular pentagon, we need to divide the perimeter by the number of sides. A regular pentagon has 5 sides.
Given:
- Perimeter of the pentagon = 50 meters
- Number of sides = 5
We calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{50 \text{ meters}}{5}
\]
\[
\text{Length of each side} = 10 \text{ meters}
\]
### Answer: 10 meters
Expected answer: 10
Correct? Yes
Problem: A regular nonagon has a perimeter of 63m. What is the length of each side?
GPT-4o:
A regular nonagon has 9 equal sides. To find the length of each side, we divide the perimeter by the number of sides.
Given:
- Perimeter of the nonagon = 63 meters
- Number of sides = 9
Length of each side = Perimeter / Number of sides
\[ \text{Length of each side} = \frac{63 \text{ meters}}{9} = 7 \text{ meters} \]
### Answer: 7 meters
Expected answer: 7
Correct? Yes
Problem: A regular hexagon has a perimeter of 354m. What is the length of one side of this hexagon?
GPT-4o:
To find the length of one side of a regular hexagon, we need to remember that a regular hexagon has six equal sides.
Given the perimeter of the hexagon is 354 meters, we can divide this perimeter by the number of sides to find the length of one side.
\[
\text{Length of one side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{354 \, \text{m}}{6}
\]
Performing the division:
\[
\frac{354}{6} = 59 \, \text{m}
\]
### Answer: 59 meters
Expected answer: 59
Correct? Yes
Problem: A polygon has side lengths of 59m, 16m, 15m, 35m, 89m, 16m, 43m and 7m. If the total perimeter of the polygon is 286m, what is the length of the last unknown side?
GPT-4o:
To find the length of the last unknown side, we first need to sum the known side lengths and then subtract this sum from the total perimeter. The known side lengths are: 59m, 16m, 15m, 35m, 89m, 16m, 43m, and 7m. First, we add these lengths together: \[ 59 + 16 + 15 + 35 + 89 + 16 + 43 + 7 \] Let's break it down step-by-step: \[ 59 + 16 = 75 \] \[ 75 + 15 = 90 \] \[ 90 + 35 = 125 \] \[ 125 + 89 = 214 \] \[ 214 + 16 = 230 \] \[ 230 + 43 = 273 \] \[ 273 + 7 = 280 \] The sum of the known side lengths is 280m. The total perimeter of the polygon is 286m. To find the length of the last unknown side, we subtract the sum of the known side lengths from the total perimeter: \[ 286 - 280 = 6 \] ### Answer: 6m
Expected answer: 6
Correct? Yes
Problem: A regular heptagon (7-sided polygon) has a perimeter of 616m. What is the length of each side?
GPT-4o:
To find the length of each side of a regular heptagon, we need to divide the perimeter by the number of sides.
The perimeter of the heptagon is 616 meters, and a heptagon has 7 sides.
So, the length of each side is:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{616 \, \text{m}}{7}
\]
Performing the division:
\[
\frac{616}{7} = 88 \, \text{m}
\]
### Answer: 88 meters
Expected answer: 88
Correct? Yes
Problem: A regular hexagon has a perimeter of 36m. What is the length of each side?
GPT-4o:
To find the length of each side of a regular hexagon, we need to remember that a regular hexagon has 6 equal sides.
Given the perimeter of the hexagon is 36 meters, we can set up the following equation:
\[ \text{Perimeter} = 6 \times \text{side length} \]
Let \( s \) be the length of each side. Then:
\[ 6s = 36 \]
To find \( s \), we divide both sides of the equation by 6:
\[ s = \frac{36}{6} \]
\[ s = 6 \]
### Answer: 6 meters
Expected answer: 6
Correct? Yes
Problem: A dodecagon has 11 of its 12 sides already measured. The lengths are 88cm, 24cm, 83cm, 64cm, 16cm, 14cm, 90cm, 36cm, and 47cm respectively. If the total perimeter of the dodecagon is 492cm, what is the length of the twelfth side?
GPT-4o:
To find the length of the twelfth side of the dodecagon, we first need to sum the lengths of the 11 known sides. The given lengths are: 88 cm, 24 cm, 83 cm, 64 cm, 16 cm, 14 cm, 90 cm, 36 cm, 47 cm, 30 cm, and 0 cm. First, let's sum these lengths: \[ 88 + 24 + 83 + 64 + 16 + 14 + 90 + 36 + 47 + 30 + 0 = 492 \] The total perimeter of the dodecagon is given as 492 cm. Therefore, the length of the twelfth side is: \[ 492 - 492 = 0 \] ### Answer: 0
Expected answer: 30
Correct? No
Problem: A regular hexagon has a perimeter of 306m. What is the length of each side?
GPT-4o:
To find the length of each side of a regular hexagon, we need to remember that a regular hexagon has 6 equal sides.
Given the perimeter of the hexagon is 306 meters, we can set up the following equation:
\[ \text{Perimeter} = 6 \times \text{side length} \]
Let \( s \) be the length of each side. Then:
\[ 6s = 306 \]
To find \( s \), we divide both sides of the equation by 6:
\[ s = \frac{306}{6} \]
\[ s = 51 \]
### Answer: 51 meters
Expected answer: 51
Correct? Yes
Problem: A regular heptagon (7-sided polygon) has a perimeter of 238 meters. What is the length of each side?
GPT-4o:
To find the length of each side of a regular heptagon, we need to divide the perimeter by the number of sides.
A regular heptagon has 7 sides, and the perimeter is given as 238 meters.
The length of each side is calculated as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{238 \text{ meters}}{7}
\]
Performing the division:
\[
\frac{238}{7} = 34 \text{ meters}
\]
### Answer: 34 meters
Expected answer: 34
Correct? Yes
Problem: A regular hexagon has a total perimeter of 42m. What is the length of each side?
GPT-4o:
To find the length of each side of a regular hexagon, we need to remember that a regular hexagon has 6 equal sides.
Given the total perimeter of the hexagon is 42 meters, we can set up the following equation:
\[ \text{Perimeter} = 6 \times \text{side length} \]
Let \( s \) be the length of each side. Then:
\[ 6s = 42 \]
To find \( s \), we divide both sides of the equation by 6:
\[ s = \frac{42}{6} \]
\[ s = 7 \]
### Answer: 7 meters
Expected answer: 7
Correct? Yes
Problem: A regular octagon has a perimeter of 624m. What is the length of each side of the octagon?
GPT-4o:
To find the length of each side of a regular octagon, we need to divide the perimeter by the number of sides. A regular octagon has 8 sides.
Given the perimeter is 624 meters, we calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{624 \, \text{m}}{8}
\]
Performing the division:
\[
\frac{624}{8} = 78 \, \text{m}
\]
### Answer: 78 m
Expected answer: 78
Correct? Yes
Problem: A polygon with nine sides has lengths of 17m, 13m, 61m, 16m, 11m, 83m, 28m, 48m, and 93m. What is the length of the tenth side if the total perimeter of the polygon is 468 meters?
GPT-4o:
To find the length of the tenth side of the polygon, we first need to determine the sum of the lengths of the given nine sides. The lengths of the nine sides are: 17m, 13m, 61m, 16m, 11m, 83m, 28m, 48m, and 93m. Let's add these lengths together: \[ 17 + 13 + 61 + 16 + 11 + 83 + 28 + 48 + 93 \] First, we can group and add them step by step: \[ 17 + 13 = 30 \] \[ 30 + 61 = 91 \] \[ 91 + 16 = 107 \] \[ 107 + 11 = 118 \] \[ 118 + 83 = 201 \] \[ 201 + 28 = 229 \] \[ 229 + 48 = 277 \] \[ 277 + 93 = 370 \] The sum of the lengths of the nine sides is 370 meters. The total perimeter of the polygon is given as 468 meters. To find the length of the tenth side, we subtract the sum of the nine sides from the total perimeter: \[ 468 - 370 = 98 \] ### Answer: 98 meters
Expected answer: 98
Correct? Yes
Problem: A regular pentagon has a perimeter of 380m. What is the length of each side?
GPT-4o:
To find the length of each side of a regular pentagon, we need to divide the perimeter by the number of sides. A regular pentagon has 5 sides. Given: Perimeter = 380 meters Length of each side = Perimeter / Number of sides Length of each side = 380 meters / 5 Calculating the division: \[ 380 \div 5 = 76 \] ### Answer: 76 meters
Expected answer: 76
Correct? Yes
Problem: A regular octagon has a perimeter of 104cm. What is the length of one of its sides?
GPT-4o:
To find the length of one side of a regular octagon, we need to divide the perimeter by the number of sides. A regular octagon has 8 sides.
Given the perimeter is 104 cm, we calculate the length of one side as follows:
\[
\text{Length of one side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{104 \, \text{cm}}{8}
\]
\[
\text{Length of one side} = 13 \, \text{cm}
\]
### Answer: 13 cm
Expected answer: 13
Correct? Yes
Problem: A regular heptagon (7-sided polygon) has a perimeter of 637m. What is the length of each side?
GPT-4o:
To find the length of each side of a regular heptagon, we need to divide the perimeter by the number of sides.
Given:
- Perimeter of the heptagon = 637 meters
- Number of sides in a heptagon = 7
We calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{637 \text{ meters}}{7}
\]
Performing the division:
\[
\frac{637}{7} = 91 \text{ meters}
\]
### Answer: 91 meters
Expected answer: 91
Correct? Yes
Problem: A regular pentagon has a perimeter of 35m. What is the length of each side?
GPT-4o:
To find the length of each side of a regular pentagon, we need to divide the perimeter by the number of sides. A regular pentagon has 5 sides.
Given:
- Perimeter of the pentagon = 35 meters
- Number of sides = 5
We calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{35 \, \text{m}}{5}
\]
\[
\text{Length of each side} = 7 \, \text{m}
\]
### Answer: 7 meters
Expected answer: 7
Correct? Yes
Problem: The perimeter of a pentagon is 223cm. The lengths of four of its sides are 45cm, 93cm, 36cm, and 22cm respectively. What is the length of the fifth side?
GPT-4o:
To find the length of the fifth side of the pentagon, we need to subtract the sum of the lengths of the known four sides from the total perimeter.
First, let's add the lengths of the four known sides:
\[ 45 \, \text{cm} + 93 \, \text{cm} + 36 \, \text{cm} + 22 \, \text{cm} \]
Calculating the sum:
\[ 45 + 93 = 138 \]
\[ 138 + 36 = 174 \]
\[ 174 + 22 = 196 \]
The sum of the lengths of the four sides is 196 cm.
Next, we subtract this sum from the total perimeter to find the length of the fifth side:
\[ 223 \, \text{cm} - 196 \, \text{cm} = 27 \, \text{cm} \]
### Answer: 27 cm
Expected answer: 27
Correct? Yes
Problem: A polygon has sides measuring 75cm, 81cm, 22cm, 94cm, 91cm, and 10cm. If the perimeter of the polygon is 423cm, what is the length of the last unknown side?
GPT-4o:
To find the length of the last unknown side, we first need to sum the known side lengths of the polygon and then subtract this sum from the total perimeter. The known side lengths are: 75 cm, 81 cm, 22 cm, 94 cm, 91 cm, and 10 cm. First, we add these known side lengths together: \[ 75 + 81 + 22 + 94 + 91 + 10 \] Let's perform the addition step-by-step: \[ 75 + 81 = 156 \] \[ 156 + 22 = 178 \] \[ 178 + 94 = 272 \] \[ 272 + 91 = 363 \] \[ 363 + 10 = 373 \] The sum of the known side lengths is 373 cm. The total perimeter of the polygon is given as 423 cm. To find the length of the last unknown side, we subtract the sum of the known side lengths from the total perimeter: \[ 423 - 373 = 50 \] ### Answer: 50 cm
Expected answer: 50
Correct? Yes
Problem: A regular decagon (10-sided polygon) has a perimeter of 600m. What is the length of each side?
GPT-4o:
To find the length of each side of a regular decagon, we need to divide the perimeter by the number of sides.
A regular decagon has 10 sides. Given that the perimeter is 600 meters, we can calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{600 \text{ meters}}{10}
\]
\[
\text{Length of each side} = 60 \text{ meters}
\]
### Answer: 60 meters
Expected answer: 60
Correct? Yes
Problem: The perimeter of a regular octagon is 632m. What is the length of each of its sides?
GPT-4o:
To find the length of each side of a regular octagon, we need to divide the perimeter by the number of sides. A regular octagon has 8 sides.
Given:
- Perimeter of the octagon = 632 meters
- Number of sides = 8
We calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{632 \, \text{m}}{8}
\]
Performing the division:
\[
\frac{632}{8} = 79 \, \text{m}
\]
### Answer: 79 meters
Expected answer: 79
Correct? Yes
Problem: A regular septagon (7-sided polygon) has a total perimeter of 161m. What is the length of each side?
GPT-4o:
To find the length of each side of a regular septagon, we need to divide the total perimeter by the number of sides.
A regular septagon has 7 sides, and the total perimeter is 161 meters.
The length of each side is calculated as follows:
\[
\text{Length of each side} = \frac{\text{Total perimeter}}{\text{Number of sides}} = \frac{161 \, \text{m}}{7}
\]
Performing the division:
\[
\frac{161}{7} = 23 \, \text{m}
\]
### Answer: 23 meters
Expected answer: 23
Correct? Yes
Problem: A regular hexagon has a perimeter of 96m. What is the length of each side?
GPT-4o:
To find the length of each side of a regular hexagon, we need to remember that a regular hexagon has 6 equal sides.
Given the perimeter of the hexagon is 96 meters, we can set up the following equation:
\[ \text{Perimeter} = 6 \times \text{side length} \]
Let \( s \) be the length of each side. Then:
\[ 6s = 96 \]
To find \( s \), we divide both sides of the equation by 6:
\[ s = \frac{96}{6} \]
\[ s = 16 \]
### Answer: 16 meters
Expected answer: 16
Correct? Yes
Problem: A nonagon (9-sided polygon), has sides with length 50m, 31m, 24m, 28m, 13m, 97m, 63m and 88m. Find the length of the ninth side if the total perimeter of the nonagon is 402m.
GPT-4o:
To find the length of the ninth side of the nonagon, we first need to sum the lengths of the given eight sides and then subtract this sum from the total perimeter. The given side lengths are: 50m, 31m, 24m, 28m, 13m, 97m, 63m, and 88m. First, we sum these lengths: \[ 50 + 31 + 24 + 28 + 13 + 97 + 63 + 88 \] Let's add them step by step: \[ 50 + 31 = 81 \] \[ 81 + 24 = 105 \] \[ 105 + 28 = 133 \] \[ 133 + 13 = 146 \] \[ 146 + 97 = 243 \] \[ 243 + 63 = 306 \] \[ 306 + 88 = 394 \] The sum of the given eight sides is 394 meters. The total perimeter of the nonagon is 402 meters. To find the length of the ninth side, we subtract the sum of the eight sides from the total perimeter: \[ 402 - 394 = 8 \] ### Answer: 8 meters
Expected answer: 8
Correct? Yes
Problem: A regular heptagon (7-sided polygon) has a perimeter of 385m. What is the length of each side?
GPT-4o:
To find the length of each side of a regular heptagon, we need to divide the perimeter by the number of sides.
The perimeter of the heptagon is 385 meters, and a heptagon has 7 sides.
So, the length of each side is:
\[ \text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{385 \, \text{m}}{7} \]
Performing the division:
\[ \frac{385}{7} = 55 \, \text{m} \]
### Answer: 55 meters
Expected answer: 55
Correct? Yes
Problem: The total perimeter of a polygon is 358 meters. The lengths of five of its sides are 89 meters, 2 meters, 10 meters, 48 meters, and 94 meters respectively, and another side measures 59 meters. What is the length of the remaining side?
GPT-4o:
To find the length of the remaining side, we first need to sum the lengths of the known sides and then subtract this sum from the total perimeter. The lengths of the known sides are: - 89 meters - 2 meters - 10 meters - 48 meters - 94 meters - 59 meters First, we add these lengths together: \[ 89 + 2 + 10 + 48 + 94 + 59 \] Let's perform the addition step-by-step: \[ 89 + 2 = 91 \] \[ 91 + 10 = 101 \] \[ 101 + 48 = 149 \] \[ 149 + 94 = 243 \] \[ 243 + 59 = 302 \] The sum of the known sides is 302 meters. Next, we subtract this sum from the total perimeter to find the length of the remaining side: \[ 358 - 302 = 56 \] ### Answer: 56 meters.
Expected answer: 56
Correct? Yes
Problem: An octagon has a equal sides and its total perimeter is 496m. What is the length of each side?
GPT-4o:
To find the length of each side of the octagon, we need to divide the total perimeter by the number of sides. An octagon has 8 sides.
Given:
- Total perimeter = 496 meters
- Number of sides = 8
We calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Total perimeter}}{\text{Number of sides}} = \frac{496 \, \text{meters}}{8}
\]
Performing the division:
\[
\frac{496}{8} = 62 \, \text{meters}
\]
### Answer: 62 meters
Expected answer: 62
Correct? Yes
Problem: A regular octagon has a perimeter of 800m. What is the length of each side?
GPT-4o:
To find the length of each side of a regular octagon, we need to divide the perimeter by the number of sides. A regular octagon has 8 sides.
Given the perimeter is 800 meters, we calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{800 \, \text{m}}{8}
\]
\[
\text{Length of each side} = 100 \, \text{m}
\]
### Answer: 100 meters
Expected answer: 100
Correct? Yes
Problem: A regular nonagon has a certain side length. If the perimeter of the nonagon is 702 m, what is the length of one side?
GPT-4o:
To find the length of one side of a regular nonagon, we need to know that a nonagon has 9 sides. The perimeter of a regular polygon is the sum of the lengths of all its sides.
Given:
- Perimeter of the nonagon = 702 meters
- Number of sides = 9
We can find the length of one side by dividing the perimeter by the number of sides:
\[
\text{Length of one side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{702 \, \text{m}}{9}
\]
Now, perform the division:
\[
\frac{702}{9} = 78 \, \text{m}
\]
### Answer: 78 m
Expected answer: 78
Correct? Yes
Problem: A regular nonagon has a perimeter of 855cm. What is the length of one side?
GPT-4o:
To find the length of one side of a regular nonagon, we need to know that a nonagon has 9 sides.
Given the perimeter of the nonagon is 855 cm, we can find the length of one side by dividing the perimeter by the number of sides.
\[
\text{Length of one side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{855 \, \text{cm}}{9}
\]
Now, perform the division:
\[
\frac{855}{9} = 95 \, \text{cm}
\]
### Answer: 95 cm
Expected answer: 95
Correct? Yes
Problem: If a regular heptagon has a perimeter of 504 meters, find the length of its side.
GPT-4o:
To find the length of a side of a regular heptagon, we need to know that a regular heptagon has 7 equal sides.
Given the perimeter of the heptagon is 504 meters, we can use the formula for the perimeter of a regular polygon:
\[ \text{Perimeter} = \text{Number of sides} \times \text{Length of one side} \]
Let \( s \) be the length of one side. For a heptagon, the number of sides is 7. Therefore:
\[ 504 = 7 \times s \]
To find \( s \), we divide both sides of the equation by 7:
\[ s = \frac{504}{7} \]
Calculating the division:
\[ s = 72 \]
### Answer: 72 meters
Expected answer: 72
Correct? Yes
Problem: A regular nonagon has a perimeter of 657m. What is the length of each side?
GPT-4o:
To find the length of each side of a regular nonagon, we need to divide the perimeter by the number of sides. A nonagon has 9 sides.
Given:
- Perimeter of the nonagon = 657 meters
- Number of sides = 9
We calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{657 \, \text{m}}{9}
\]
Perform the division:
\[
\frac{657}{9} = 73 \, \text{m}
\]
### Answer: 73 meters
Expected answer: 73
Correct? Yes
Problem: Given a regular octagon where the total perimeter is 48 cm, what is the length of each side?
GPT-4o:
To find the length of each side of a regular octagon, we need to divide the total perimeter by the number of sides. A regular octagon has 8 sides.
Given:
- Total perimeter = 48 cm
- Number of sides = 8
We calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Total perimeter}}{\text{Number of sides}} = \frac{48 \, \text{cm}}{8}
\]
\[
\text{Length of each side} = 6 \, \text{cm}
\]
### Answer: 6 cm
Expected answer: 6
Correct? Yes
Problem: A polygon has eight sides with lengths: 28m, 37m, 51m, 84m, 54m, 31m, 94m, and 12m. If the total perimeter of the polygon is 399m, what is the length of the remaining unknown side?
GPT-4o:
To find the length of the remaining unknown side, we first need to sum the lengths of the known sides and then subtract this sum from the total perimeter. The known side lengths are: 28m, 37m, 51m, 84m, 54m, 31m, 94m, and 12m. First, we sum these lengths: \[ 28 + 37 + 51 + 84 + 54 + 31 + 94 + 12 \] Let's add them step by step: \[ 28 + 37 = 65 \] \[ 65 + 51 = 116 \] \[ 116 + 84 = 200 \] \[ 200 + 54 = 254 \] \[ 254 + 31 = 285 \] \[ 285 + 94 = 379 \] \[ 379 + 12 = 391 \] The sum of the known side lengths is 391m. The total perimeter of the polygon is 399m. To find the length of the remaining unknown side, we subtract the sum of the known side lengths from the total perimeter: \[ 399 - 391 = 8 \] ### Answer: 8m
Expected answer: 8
Correct? Yes
Problem: A regular nonagon has a perimeter of 342m. What is the length of one side?
GPT-4o:
To find the length of one side of a regular nonagon, we need to divide the perimeter by the number of sides. A nonagon has 9 sides.
Given:
- Perimeter of the nonagon = 342 meters
- Number of sides = 9
We calculate the length of one side as follows:
\[ \text{Length of one side} = \frac{\text{Perimeter}}{\text{Number of sides}} \]
\[ \text{Length of one side} = \frac{342 \, \text{m}}{9} \]
\[ \text{Length of one side} = 38 \, \text{m} \]
### Answer: 38 meters
Expected answer: 38
Correct? Yes
Problem: In a polygon with 8 sides, 7 of the side lengths are given as follows: 7 m, 59 m, 49 m, 38 m, 53 m, 21 m, and 34 m. Given that the total perimeter of the polygon is 330 m, what is the length of the eighth side?
GPT-4o:
To find the length of the eighth side of the polygon, we first need to determine the sum of the given side lengths. The given side lengths are: 7 m, 59 m, 49 m, 38 m, 53 m, 21 m, and 34 m. Let's add these lengths together: \[ 7 + 59 + 49 + 38 + 53 + 21 + 34 \] First, we add the numbers step by step: \[ 7 + 59 = 66 \] \[ 66 + 49 = 115 \] \[ 115 + 38 = 153 \] \[ 153 + 53 = 206 \] \[ 206 + 21 = 227 \] \[ 227 + 34 = 261 \] So, the sum of the given side lengths is 261 meters. The total perimeter of the polygon is given as 330 meters. To find the length of the eighth side, we subtract the sum of the given side lengths from the total perimeter: \[ 330 - 261 = 69 \] ### Answer: 69 meters
Expected answer: 69
Correct? Yes
Problem: A decagon has side lengths of 88m, 96m, 74m, 52m, 45m, 74m, 85m, 85m, and 43m. What is the length of the tenth side if the total perimeter of the decagon is 682m?
GPT-4o:
To find the length of the tenth side of the decagon, we first need to sum the lengths of the nine given sides and then subtract this sum from the total perimeter. The given side lengths are: 88m, 96m, 74m, 52m, 45m, 74m, 85m, 85m, and 43m. First, we sum these lengths: \[ 88 + 96 + 74 + 52 + 45 + 74 + 85 + 85 + 43 \] Let's add them step by step: \[ 88 + 96 = 184 \] \[ 184 + 74 = 258 \] \[ 258 + 52 = 310 \] \[ 310 + 45 = 355 \] \[ 355 + 74 = 429 \] \[ 429 + 85 = 514 \] \[ 514 + 85 = 599 \] \[ 599 + 43 = 642 \] The sum of the nine given sides is 642 meters. The total perimeter of the decagon is 682 meters. To find the length of the tenth side, we subtract the sum of the nine sides from the total perimeter: \[ 682 - 642 = 40 \] ### Answer: 40 meters
Expected answer: 40
Correct? Yes
Problem: A regular septagon (7-sided polygon) has a constant perimeter of 161m. If all sides are equal, what is the length of each side?
GPT-4o:
To find the length of each side of a regular septagon, we need to divide the total perimeter by the number of sides.
The perimeter of the septagon is 161 meters, and it has 7 sides.
Length of each side = Total perimeter / Number of sides
\[ \text{Length of each side} = \frac{161 \text{ meters}}{7} \]
Now, we perform the division:
\[ \frac{161}{7} = 23 \]
So, the length of each side of the regular septagon is 23 meters.
### Answer: 23 meters
Expected answer: 23
Correct? Yes
Problem: A regular hexagon has a perimeter of 324m. What is the length of each side?
GPT-4o:
To find the length of each side of a regular hexagon, we need to remember that a regular hexagon has 6 equal sides.
Given the perimeter of the hexagon is 324 meters, we can set up the following equation:
\[ \text{Perimeter} = 6 \times \text{side length} \]
Let \( s \) be the length of each side. Then:
\[ 6s = 324 \]
To find \( s \), we divide both sides of the equation by 6:
\[ s = \frac{324}{6} \]
Calculating the division:
\[ s = 54 \]
So, the length of each side of the hexagon is 54 meters.
### Answer: 54 meters
Expected answer: 54
Correct? Yes
Problem: A regular pentagon's perimeter is 385 meters. What is the length of one side?
GPT-4o:
To find the length of one side of a regular pentagon, we need to divide the perimeter by the number of sides. A regular pentagon has 5 sides.
Given:
- Perimeter of the pentagon = 385 meters
- Number of sides = 5
We calculate the length of one side as follows:
\[
\text{Length of one side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{385 \text{ meters}}{5}
\]
Performing the division:
\[
\frac{385}{5} = 77 \text{ meters}
\]
### Answer: 77 meters
Expected answer: 77
Correct? Yes
Problem: A regular septagon (7-sided polygon) has a perimeter of 245m. What is the length of each side?
GPT-4o:
To find the length of each side of a regular septagon, we need to divide the perimeter by the number of sides.
Given:
- Perimeter of the septagon = 245 meters
- Number of sides in a septagon = 7
We use the formula for the length of each side:
\[ \text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} \]
Substituting the given values:
\[ \text{Length of each side} = \frac{245 \text{ meters}}{7} \]
Performing the division:
\[ \text{Length of each side} = 35 \text{ meters} \]
### Answer: 35 meters
Expected answer: 35
Correct? Yes
Problem: A regular pentagon has a perimeter of 25cm. What is the length of one of its sides?
GPT-4o:
To find the length of one side of a regular pentagon, we need to divide the perimeter by the number of sides. A regular pentagon has 5 sides.
Given:
- Perimeter of the pentagon = 25 cm
- Number of sides = 5
We calculate the length of one side as follows:
\[
\text{Length of one side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{25 \, \text{cm}}{5}
\]
\[
\text{Length of one side} = 5 \, \text{cm}
\]
### Answer: 5 cm
Expected answer: 5
Correct? Yes
Problem: A regular hexagon has five of its sides measuring 9m, 49m, 100m, 73m, and 84m respectively. If the total perimeter of the hexagon is 380m, find the length of the sixth side.
GPT-4o:
To find the length of the sixth side of the hexagon, we first need to understand that the perimeter of a hexagon is the sum of the lengths of all its sides. Given: - Five sides of the hexagon measure 9m, 49m, 100m, 73m, and 84m. - The total perimeter of the hexagon is 380m. First, we sum the lengths of the five given sides: \[ 9 + 49 + 100 + 73 + 84 = 315 \] Next, we subtract this sum from the total perimeter to find the length of the sixth side: \[ 380 - 315 = 65 \] Thus, the length of the sixth side is 65 meters. ### Answer: 65m
Expected answer: 65
Correct? Yes
Problem: An irregular polygon has seven sides with lengths of 23m, 67m, 57m, 94m, 93m, 18m and 30m respectively. If the total perimeter of the polygon is 419m, what is the length of the missing side?
GPT-4o:
To find the length of the missing side, we first need to sum the lengths of the given sides and then subtract this sum from the total perimeter. The given side lengths are: 23m, 67m, 57m, 94m, 93m, 18m, and 30m. First, we sum these lengths: \[ 23 + 67 + 57 + 94 + 93 + 18 + 30 \] Let's add them step by step: \[ 23 + 67 = 90 \] \[ 90 + 57 = 147 \] \[ 147 + 94 = 241 \] \[ 241 + 93 = 334 \] \[ 334 + 18 = 352 \] \[ 352 + 30 = 382 \] The sum of the given side lengths is 382m. The total perimeter of the polygon is 419m. To find the length of the missing side, we subtract the sum of the given sides from the total perimeter: \[ 419 - 382 = 37 \] ### Answer: 37m
Expected answer: 37
Correct? Yes
Problem: A regular heptagon (7-sided polygon) has a perimeter of 287m. What is the length of each side?
GPT-4o:
To find the length of each side of a regular heptagon, we need to divide the perimeter by the number of sides.
The perimeter of the heptagon is 287 meters, and a heptagon has 7 sides.
So, the length of each side is:
\[ \text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{287 \, \text{m}}{7} \]
Now, we perform the division:
\[ \frac{287}{7} = 41 \]
### Answer: 41 meters
Expected answer: 41
Correct? Yes
Problem: A regular pentagon has a perimeter of 55m. What is the length of each side?
GPT-4o:
To find the length of each side of a regular pentagon, we need to divide the perimeter by the number of sides. A regular pentagon has 5 sides. Given: Perimeter = 55 meters Length of each side = Perimeter / Number of sides Length of each side = 55 meters / 5 Length of each side = 11 meters ### Answer: 11 meters
Expected answer: 11
Correct? Yes
Problem: A regular nonagon, which is a nine-sided polygon, has equal side lengths. If the entire perimeter of the nonagon is 657 meters, how long is each side?
GPT-4o:
To find the length of each side of a regular nonagon, we need to divide the total perimeter by the number of sides.
The perimeter of the nonagon is given as 657 meters, and a nonagon has 9 sides.
So, the length of each side is calculated as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{657 \text{ meters}}{9}
\]
Performing the division:
\[
\frac{657}{9} = 73 \text{ meters}
\]
### Answer: 73 meters
Expected answer: 73
Correct? Yes
Problem: A regular hexagon has a perimeter of 78m. What is the length of each side?
GPT-4o:
To find the length of each side of a regular hexagon, we need to remember that a regular hexagon has six equal sides.
Given that the perimeter of the hexagon is 78 meters, we can set up the following equation to find the length of one side:
\[ \text{Perimeter} = 6 \times \text{side length} \]
Substituting the given perimeter:
\[ 78 = 6 \times \text{side length} \]
To find the side length, we divide both sides of the equation by 6:
\[ \text{side length} = \frac{78}{6} \]
\[ \text{side length} = 13 \]
### Answer: 13 meters
Expected answer: 13
Correct? Yes
Problem: A regular octagon has a total perimeter of 600 meters. What is the length of one of its sides?
GPT-4o:
To find the length of one side of a regular octagon, we need to divide the total perimeter by the number of sides. A regular octagon has 8 sides.
Given:
Total perimeter = 600 meters
We calculate the length of one side as follows:
\[
\text{Length of one side} = \frac{\text{Total perimeter}}{\text{Number of sides}} = \frac{600 \text{ meters}}{8}
\]
Performing the division:
\[
\frac{600}{8} = 75 \text{ meters}
\]
### Answer: 75 meters
Expected answer: 75
Correct? Yes
Problem: A polygon has side lengths of 39m, 26m, 47m, 52m, 66m, 17m, and 34m. If the overall perimeter of the polygon is 356m, what is the length of the last side?
GPT-4o:
To find the length of the last side of the polygon, we need to first sum the given side lengths and then subtract this sum from the total perimeter. First, let's add the given side lengths: \[ 39 + 26 + 47 + 52 + 66 + 17 + 34 \] Calculating step-by-step: \[ 39 + 26 = 65 \] \[ 65 + 47 = 112 \] \[ 112 + 52 = 164 \] \[ 164 + 66 = 230 \] \[ 230 + 17 = 247 \] \[ 247 + 34 = 281 \] The sum of the given side lengths is 281 meters. Next, we subtract this sum from the total perimeter to find the length of the last side: \[ 356 - 281 = 75 \] ### Answer: 75 meters
Expected answer: 75
Correct? Yes
Problem: A regular decagon has a perimeter of 930 cm. What is the length of each side?
GPT-4o:
To find the length of each side of a regular decagon, we need to know that a regular decagon has 10 equal sides.
Given the perimeter of the decagon is 930 cm, we can find the length of each side by dividing the perimeter by the number of sides.
\[
\text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{930 \, \text{cm}}{10}
\]
\[
\text{Length of each side} = 93 \, \text{cm}
\]
### Answer: 93 cm
Expected answer: 93
Correct? Yes
Problem: A decagon has eight of its sides measuring 24m, 25m, 75m, 38m, 18m, 42m and 61m. If the total perimeter of the decagon is 359m, can you find the length of one of the unknown sides?
GPT-4o:
To find the length of one of the unknown sides of the decagon, we first need to sum the lengths of the known sides. The known sides are 24m, 25m, 75m, 38m, 18m, 42m, and 61m. Let's add these lengths together: \[ 24 + 25 + 75 + 38 + 18 + 42 + 61 \] First, add 24 and 25: \[ 24 + 25 = 49 \] Next, add 49 and 75: \[ 49 + 75 = 124 \] Next, add 124 and 38: \[ 124 + 38 = 162 \] Next, add 162 and 18: \[ 162 + 18 = 180 \] Next, add 180 and 42: \[ 180 + 42 = 222 \] Finally, add 222 and 61: \[ 222 + 61 = 283 \] The sum of the known sides is 283 meters. The total perimeter of the decagon is 359 meters. To find the total length of the unknown sides, we subtract the sum of the known sides from the total perimeter: \[ 359 - 283 = 76 \] Since there are two unknown sides and their total length is 76 meters, we can divide this by 2 to find the length of one unknown side: \[ 76 \div 2 = 38 \] ### Answer: 38 meters
Expected answer: 76
Correct? No
Problem: A nonagon has side lengths of 52m, 52m, 44m, 53m, 41m, 91m, 25m, and 2m and the total perimeter of the nonagon is 368m. What is the length of the final side?
GPT-4o:
To find the length of the final side of the nonagon, we first need to sum the lengths of the given sides and then subtract this sum from the total perimeter. Given side lengths: 52m, 52m, 44m, 53m, 41m, 91m, 25m, and 2m. First, we sum these lengths: \[ 52 + 52 + 44 + 53 + 41 + 91 + 25 + 2 \] Let's add them step by step: \[ 52 + 52 = 104 \] \[ 104 + 44 = 148 \] \[ 148 + 53 = 201 \] \[ 201 + 41 = 242 \] \[ 242 + 91 = 333 \] \[ 333 + 25 = 358 \] \[ 358 + 2 = 360 \] The sum of the given side lengths is 360 meters. The total perimeter of the nonagon is 368 meters. To find the length of the final side, we subtract the sum of the given side lengths from the total perimeter: \[ 368 - 360 = 8 \] ### Answer: 8 meters
Expected answer: 8
Correct? Yes
Problem: A regular octagon has a perimeter of 592cm. What is the length of one side?
GPT-4o:
To find the length of one side of a regular octagon, we need to divide the perimeter by the number of sides. A regular octagon has 8 sides.
Given the perimeter is 592 cm, we calculate the length of one side as follows:
\[
\text{Length of one side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{592 \, \text{cm}}{8}
\]
Performing the division:
\[
\frac{592}{8} = 74 \, \text{cm}
\]
### Answer: 74 cm
Expected answer: 74
Correct? Yes
Problem: A regular heptagon has a perimeter of 245m. What is the length of each side?
GPT-4o:
To find the length of each side of a regular heptagon, we need to divide the perimeter by the number of sides. A heptagon has 7 sides.
Given:
- Perimeter of the heptagon = 245 meters
- Number of sides = 7
We calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{245 \text{ meters}}{7}
\]
Performing the division:
\[
\frac{245}{7} = 35 \text{ meters}
\]
### Answer: 35 meters
Expected answer: 35
Correct? Yes
Problem: A regular decagon has a perimeter of 140m. What is the length of each side?
GPT-4o:
A regular decagon has 10 equal sides. To find the length of each side, we need to divide the total perimeter by the number of sides.
Given:
- Perimeter of the decagon = 140 meters
- Number of sides = 10
Length of each side = Perimeter / Number of sides
\[ \text{Length of each side} = \frac{140 \text{ meters}}{10} = 14 \text{ meters} \]
### Answer: 14 meters
Expected answer: 14
Correct? Yes
Problem: A polygon has side lengths of 44cm, 5cm, 96cm, 78cm, 49cm, 84cm, 72cm, 74cm, 21cm, and 39cm. If the total perimeter of the polygon is 655cm. What is the length of its 11th side?
GPT-4o:
To find the length of the 11th side of the polygon, we first need to determine the sum of the given side lengths. The given side lengths are: 44 cm, 5 cm, 96 cm, 78 cm, 49 cm, 84 cm, 72 cm, 74 cm, 21 cm, and 39 cm. Let's add these lengths together: \[ 44 + 5 + 96 + 78 + 49 + 84 + 72 + 74 + 21 + 39 \] First, we can add them step by step: \[ 44 + 5 = 49 \] \[ 49 + 96 = 145 \] \[ 145 + 78 = 223 \] \[ 223 + 49 = 272 \] \[ 272 + 84 = 356 \] \[ 356 + 72 = 428 \] \[ 428 + 74 = 502 \] \[ 502 + 21 = 523 \] \[ 523 + 39 = 562 \] The sum of the given side lengths is 562 cm. The total perimeter of the polygon is given as 655 cm. To find the length of the 11th side, we subtract the sum of the given side lengths from the total perimeter: \[ 655 - 562 = 93 \] ### Answer: 93 cm
Expected answer: 93
Correct? Yes
Problem: A polygon has sides that measure 69m, 81m, 34m, 35m, and 38m respectively. If the polygon's total perimeter is 265m, what is the length of the remaining side?
GPT-4o:
To find the length of the remaining side of the polygon, we first need to sum the lengths of the given sides and then subtract this sum from the total perimeter. The given side lengths are: 69m, 81m, 34m, 35m, and 38m. First, we sum these lengths: \[ 69 + 81 + 34 + 35 + 38 \] Let's add them step by step: \[ 69 + 81 = 150 \] \[ 150 + 34 = 184 \] \[ 184 + 35 = 219 \] \[ 219 + 38 = 257 \] The sum of the given side lengths is 257 meters. The total perimeter of the polygon is 265 meters. To find the length of the remaining side, we subtract the sum of the given sides from the total perimeter: \[ 265 - 257 = 8 \] ### Answer: 8 meters
Expected answer: 8
Correct? Yes
Problem: A pentagon has four of its side lengths as 22m, 14m, 93m, and 75m respectively. If its total perimeter is 234m, find the length of the fifth side.
GPT-4o:
To find the length of the fifth side of the pentagon, we need to use the information about the total perimeter and the lengths of the other four sides.
First, let's add up the lengths of the four given sides:
\[ 22 \, \text{m} + 14 \, \text{m} + 93 \, \text{m} + 75 \, \text{m} \]
Calculating the sum:
\[ 22 + 14 = 36 \]
\[ 36 + 93 = 129 \]
\[ 129 + 75 = 204 \]
The total perimeter of the pentagon is given as 234 meters. To find the length of the fifth side, we subtract the sum of the four sides from the total perimeter:
\[ 234 \, \text{m} - 204 \, \text{m} = 30 \, \text{m} \]
### Answer: 30 meters
Expected answer: 30
Correct? Yes