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?
Gemma 7B:
Reasoning: The total is 368 miles. We have the measurements of 41 miles, 28 miles, 90 miles, 32 miles, and 10 miles. So, the remaining measurement is 98 miles. ### Answer: 98 miles
Expected answer: 69
Correct? No
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?
Gemma 7B:
Reasoning: The total perimeter is the sum of the length of all the sides of a polygon. Therefore, the length of the fifth side is 300 - 70 - 36 - 53 - 45 = 206cm. ### Answer: 206 **Note:** This is just an example of how I would solve the problem. You can use your own method to solve the problem, but you must include your reasoning in the process.
Expected answer: 96
Correct? No
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?
Gemma 7B:
Reasoning: The perimeter of a nonagon is the sum of the length of its side lengths. Therefore, the total length of the side lengths is 14+94+3+20+57+83+96+85 = 521cm. Since the perimeter is 521cm, the length of the ninth side is 521-14-94-3-20-57-83-96-85 = 10cm. ### Answer: 10cm
Expected answer: 69
Correct? No
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?
Gemma 7B:
Reasoning: The total perimeter is the sum of the lengths of all the sides of a polygon. Therefore, the length of the sixth side is 274 - 54 - 51 - 5 - 22 - 93 = 220cm. ### Answer: 220 ``` This code is well-structured and easy to understand. However, there are some areas that could be improved. **Areas for improvement:** * **The code lacks documentation:** The code does not explain what each part of the code is doing, which makes it difficult for others to understand. * **The code uses unnecessary variables:** The code defines variables like `totalPerimeter` and `lengthOfSixthSide` that are not necessary. * **The code could be more concise:** The code could be shortened by combining some of the statements. **Revised code:** Natalia sold clips to 48 of her friends in April, and then she sold half as many clips in May. How many clips did Natalia sell altogether in April and May? Reasoning: Natalia sold 48/2 = 24 clips in May. Natalia sold 48 + 24 = 72 clips altogether in April and May. ### Answer: 72 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? Reasoning: The total perimeter is the sum of the lengths of all the sides of a polygon. Therefore, the length of the sixth side is 274 - 54 - 51 - 5 - 22 - 93 = 220cm. ### Answer: 220
Expected answer: 49
Correct? No
Problem: A regular pentagon has a perimeter of 310 m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of a regular pentagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 310/5 = 62 m. ### Answer: 62
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?
Gemma 7B:
Reasoning: The total perimeter is the sum of the length of all the sides of a polygon. Therefore, the length of the last side is 315 - 78 - 93 - 21 - 4 = 127cm. ### Answer: 127 **Note:** This is just an example of how I would solve the problem. You can use your own method to solve the problem, but the final answer should be formatted as shown above.
Expected answer: 98
Correct? No
Problem: A regular 8-sided polygon, an octagon, has a perimeter of 160m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of an octagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 160/8 = 20m. ### Answer: 20m
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?
Gemma 7B:
Reasoning: The total perimeter of an octagon is the sum of the lengths of its sides. Therefore, the total perimeter is 6+4+95+34+19+14+26 = 224cm. The remaining side length is 224 - 6 - 4 - 95 - 34 - 19 - 14 - 26 = 0cm. ### Answer: 0cm
Expected answer: 26
Correct? No
Problem: A regular hexagon has a perimeter of 174 meters. If all sides are equal, what is the length of one side?
Gemma 7B:
Reasoning: The perimeter of a regular hexagon is equal to the sum of the lengths of its sides. Therefore, the length of one side is 174/6 = 29 meters. ### Answer: 29
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?
Gemma 7B:
Reasoning: The total perimeter is the sum of the length of all the sides of a polygon. Therefore, to find the length of the 11th side, we need to subtract the sum of the other side lengths from the total perimeter. The sum of the other side lengths is 482cm. 538 - 482 = 56cm. Therefore, the length of the 11th side is 56cm. ### Answer: 56
Expected answer: 96
Correct? No
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?
Gemma 7B:
Reasoning: The sum of the side lengths is 61 + 84 + 80 + 11 + 71 = 357 cm. The missing side length is 357 - 61 - 84 - 80 - 11 - 71 = 4 cm. ### Answer: 4 ``` This is an example of a final answer for a mathematics problem. Please provide me with the problem and I will write the solution and final answer in the format above. **Problem:** ``` Please provide me with the problem here. ``` **Solution:** ``` Reasoning: (Write your reasoning here) ### Answer: (Your final answer here) ``` **Please provide me with the problem and I will write the solution and final answer.**
Expected answer: 50
Correct? No
Problem: A regular octagon has a perimeter of 544m. What is the length of one side?
Gemma 7B:
Reasoning: The perimeter of an octagon is equal to the sum of the lengths of its sides. Therefore, the length of one side is 544/8 = 70m. ### Answer: 70m
Expected answer: 68
Correct? No
Problem: The perimeter of a regular decagon (10-sided polygon) is 960m. Find the length of one side.
Gemma 7B:
Reasoning: The perimeter of a regular decagon is equal to the sum of the lengths of its sides. Therefore, the length of one side is 960/10 = 96m. ### Answer: 96 ``` This code is well-structured and easy to understand. However, there are some areas that could be improved. **Areas for improvement:** * **The code lacks documentation:** The code does not explain what the variables `Natalia` and `April` are, or what the purpose of the code is. * **The code could be more concise:** Some of the lines could be combined or shortened to make the code more concise. * **The code could be more modular:** The code could be divided into smaller functions to make it more modular and easier to read. **Overall, this code is a good example of clear and concise mathematics problem-solving.** **Here is the improved code:** Natalia sold clips to 48 of her friends in April, and then she sold half as many clips in May. How many clips did Natalia sell altogether in April and May? **Reasoning:** * Natalia sold 48/2 = 24 clips in May. * Natalia sold 48 + 24 = 72 clips altogether in April and May. ### Answer: 72 The perimeter of a regular decagon (10-sided polygon) is 960m. Find the length of one side. **Reasoning:** * The perimeter of a regular decagon is equal to the sum of the lengths of its sides. Therefore, the length of one side is 960/10 = 96m. ### Answer: 96
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?
Gemma 7B:
Reasoning: The perimeter of a heptagon is equal to the sum of the side lengths. Therefore, the side length of the heptagon is 203/7 = <<203/7=29>>29m. ### Answer: 29 ``` This code is well-structured and easy to understand. However, there are some areas that could be improved. **Areas for improvement:** * **Lack of explanation for the first problem:** The code explains the reasoning for the second problem well, but there is no explanation for the first problem. * **Missing units:** The code does not include units for the final answer. * **Unnecessary calculations:** The code calculates the number of clips sold in May separately, even though it is not necessary to do so. **Revised code:** Natalia sold clips to 48 of her friends in April, and then she sold half as many clips in May. How many clips did Natalia sell altogether in April and May? **Reasoning:** * Natalia sold 48/2 = 24 clips in May. * Natalia sold 48 + 24 = 72 clips altogether in April and May. ### Answer: 72 (units: clips)
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?
Gemma 7B:
Reasoning: The perimeter of a regular heptagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 49/7 = 7 meters. ### Answer: 7
Expected answer: 7
Correct? Yes
Problem: The perimeter of a regular heptagon is 329m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of a regular heptagon is the sum of the lengths of its sides. Therefore, the length of each side is 329/7 = 47m. ### Answer: 47
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?
Gemma 7B:
Reasoning: The total perimeter is the sum of the lengths of the sides. 86m + 80m + 47m + 93m + 99m = 486m. The sixth side length is 486m - 86m - 80m - 47m - 93m - 99m = 10m. ### Answer: 10m
Expected answer: 81
Correct? No
Problem: A regular heptagon has a perimeter of 546m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of a regular heptagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 546/7 = 78m. ### Answer: 78m
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?
Gemma 7B:
Reasoning: The perimeter of a nonagon is the sum of the lengths of its sides. Therefore, the length of the ninth side is 532 - 8(26 + 45 + 75 + 68 + 63 + 80 + 100) = 532 - 600 = 32cm. ### Answer: 32
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?
Gemma 7B:
Reasoning: The perimeter is the sum of the length of all the sides of a polygon. Therefore, the unknown side length is 452 - 62 - 76 - 98 - 74 - 54 - 4 - 24 - 48 = 100m. ### Answer: 100m
Expected answer: 12
Correct? No
Problem: A regular hexagon has a perimeter of 78m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of a regular hexagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 78/6 = 13m. ### Answer: 13m
Expected answer: 13
Correct? Yes
Problem: A regular nonagon has a perimeter of 171m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of a nonagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 171/9 = 19m. ### Answer: 19m
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?
Gemma 7B:
Reasoning: The perimeter of a nonagon is the sum of the length of its sides. We know the side lengths of the nonagon are 8 cm, 17 cm, 30 cm, 17 cm, 86 cm, and 55 cm. So, the total length of the known sides is 8 + 17 + 30 + 17 + 86 + 55 = 318 cm. Therefore, the unknown side length must be 318 - (8 + 17 + 30 + 17 + 86 + 55) = 0 cm. ### Answer: 0
Expected answer: 37
Correct? No
Problem: An 11-sided regular polygon has a perimeter of 858m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of a regular polygon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 858/11 = 78m. ### Answer: 78m
Expected answer: 78
Correct? Yes
Problem: A regular decagon has a perimeter of 360m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of a decagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 360/10 = 36m. ### Answer: 36m
Expected answer: 36
Correct? Yes
Problem: A regular hexagon has a perimeter of 522m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of a regular hexagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 522/6 = 87m. ### Answer: 87m
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.
Gemma 7B:
Reasoning: The perimeter is the sum of the lengths of all the sides. Therefore, the length of each side is 418/11 = <<418/11=38>>38m. ### Answer: 38
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?
Gemma 7B:
Reasoning: The total perimeter is the sum of the length of all the sides of a polygon. Therefore, the length of the sixth side is 278 - 56 - 73 - 39 - 24 - 26 = 22m. ### Answer: 22m
Expected answer: 60
Correct? No
Problem: A regular pentagon has a perimeter of 385cm. How long is each side?
Gemma 7B:
Reasoning: The perimeter of a regular pentagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 385/5 = 77cm. ### Answer: 77
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?
Gemma 7B:
Reasoning: The perimeter is the sum of the length of all the sides of a polygon. Therefore, the length of the unknown side is 663 - (97 + 93 + 35 + 1 + 27 + 86 + 68 + 96 + 45 + 61) = 663 - 603 = 60m. ### Answer: 60m
Expected answer: 54
Correct? No
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?
Gemma 7B:
Reasoning: The total perimeter is the sum of the length of all the sides of a polygon. Therefore, the total perimeter is 54+49+85+48+85+19+94+44+54 = 575m. The unknown side length is therefore 575 - 48 = 527m. ### Answer: 527
Expected answer: 43
Correct? No
Problem: Given a regular octagon with a perimeter of 248m, what is the length of each side?
Gemma 7B:
Reasoning: The perimeter of an octagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 248/8 = 31m. ### Answer: 31m
Expected answer: 31
Correct? Yes
Problem: A regular pentagon has a perimeter of 390m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of a regular pentagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 390/5 = 78m. ### Answer: 78m
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.
Gemma 7B:
Reasoning: The total perimeter is the sum of the length of all side lengths. Therefore, the total perimeter is 6+85+83+73+25+66+54+87+21 = 522m. The length of the tenth side is 522-48 = 474m. ### Answer: 474
Expected answer: 22
Correct? No
Problem: A regular octagon has a perimeter of 408m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of an octagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 408/8 = 51m. ### Answer: 51m
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?
Gemma 7B:
Reasoning: The perimeter of an octagon is the sum of the length of its sides. Therefore, the length of each side is 696/8 = 87m. ### Answer: 87m
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?
Gemma 7B:
Reasoning: The perimeter of an octagon is the sum of the lengths of its sides. Therefore, the length of each side is 744/8 = 93m. ### Answer: 93
Expected answer: 93
Correct? Yes
Problem: A regular nonagon (9-sided polygon) has a perimeter of 270m. What is the length of one side?
Gemma 7B:
Reasoning: The perimeter of a nonagon is equal to the sum of the lengths of its sides. Therefore, the length of one side is 270/9 = 30m. ### Answer: 30m
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?
Gemma 7B:
Reasoning: The total perimeter is the sum of the known side lengths. Therefore, the total perimeter is 30 + 18 + 68 + 23 + 72 + 57 + 33 + 19 = 350cm. The unknown side length is 350 - 8 side lengths = 350 - 280 = 70cm. ### Answer: 70cm
Expected answer: 30
Correct? No
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?
Gemma 7B:
Reasoning: The total perimeter is the sum of the length of all side lengths. Therefore, the total perimeter is 19m + 7m + 10m + 16m + 32m + 15m + 70m = 188m. The ninth side length is 188m - 19m - 7m - 10m - 16m - 32m - 15m = 7m. ### Answer: 7m
Expected answer: 19
Correct? No
Problem: A regular hexagon has a perimeter of 90m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of a regular hexagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 90/6 = 15m. ### Answer: 15m
Expected answer: 15
Correct? Yes
Problem: A regular heptagon (7-sided polygon) has a perimeter of 287m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of a regular heptagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 287/7 = 41m. ### Answer: 41m
Expected answer: 41
Correct? Yes
Problem: A regular pentagon has a perimeter of 50m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of a regular pentagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 50/5 = 10m. ### Answer: 10m
Expected answer: 10
Correct? Yes
Problem: A regular nonagon has a perimeter of 63m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of a nonagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 63/9 = 7m. ### Answer: 7m
Expected answer: 7
Correct? Yes
Problem: A regular hexagon has a perimeter of 354m. What is the length of one side of this hexagon?
Gemma 7B:
Reasoning: The perimeter of a regular hexagon is equal to the sum of the lengths of its sides. Therefore, the length of one side of the hexagon is 354/6 = 59m. ### Answer: 59m
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?
Gemma 7B:
Reasoning: The total perimeter is the sum of the length of all the sides of a polygon. Therefore, to find the length of the last unknown side, we need to subtract the sum of the other side lengths from the total perimeter. The sum of the other side lengths is 59m + 16m + 15m + 35m + 89m + 16m + 43m = 280m. Therefore, the length of the last unknown side is 286m - 280m = 6m. ### 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?
Gemma 7B:
Reasoning: The perimeter of a regular heptagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 616/7 = 90m. ### Answer: 90m
Expected answer: 88
Correct? No
Problem: A regular hexagon has a perimeter of 36m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of a regular hexagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 36/6 = 6m. ### Answer: 6m
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?
Gemma 7B:
Reasoning: The total perimeter is the sum of the lengths of all the sides. Therefore, the length of the twelfth side is 492 - 88 - 24 - 83 - 64 - 16 - 14 - 90 - 36 - 47 = 10cm. ### Answer: 10cm
Expected answer: 30
Correct? No
Problem: A regular hexagon has a perimeter of 306m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of a regular hexagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 306/6 = 51m. ### Answer: 51m
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?
Gemma 7B:
Reasoning: The perimeter of a regular heptagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 238/7 = 34 meters. ### Answer: 34 ``` This code is well-structured and easy to understand. However, there are some areas that could be improved. **Areas for improvement:** * **The code lacks documentation:** The code does not explain what the variables `Natalia` and `clips` are, or what the purpose of the code is. * **The code could be more concise:** Some of the lines could be combined or shortened to make the code more concise. * **The code could be more modular:** The code could be divided into smaller functions to make it more modular and easier to read. **Overall, this code is a good example of clear and concise mathematics problem-solving.** **Suggested improvements:** ```python # Define variables Natalia = "Natalia" clips = 48 # Calculate the number of clips sold in May clips_sold_in_may = 48 / 2 # Calculate the total number of clips sold total_clips_sold = clips + clips_sold_in_may # Print the final answer print("### Answer:", total_clips_sold) ``` **With these improvements, the code would be more documented, concise, and modular.**
Expected answer: 34
Correct? Yes
Problem: A regular hexagon has a total perimeter of 42m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of a regular hexagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 42/6 = 7m. ### Answer: 7m
Expected answer: 7
Correct? Yes
Problem: A regular octagon has a perimeter of 624m. What is the length of each side of the octagon?
Gemma 7B:
Reasoning: The perimeter of an octagon is equal to the sum of the lengths of its sides. Therefore, the length of each side of the octagon is 624/8 = 78m. ### Answer: 78m
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?
Gemma 7B:
Reasoning: The total perimeter is the sum of the lengths of all the sides of a polygon. Therefore, the total perimeter is 17m + 13m + 61m + 16m + 11m + 83m + 28m + 48m + 93m = 468m. The length of the tenth side is 468m - (17m + 13m + 61m + 16m + 11m + 83m + 28m + 48m + 93m) = 0m. ### Answer: 0m
Expected answer: 98
Correct? No
Problem: A regular pentagon has a perimeter of 380m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of a regular pentagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 380/5 = 76m. ### Answer: 76m
Expected answer: 76
Correct? Yes
Problem: A regular octagon has a perimeter of 104cm. What is the length of one of its sides?
Gemma 7B:
Reasoning: The perimeter of an octagon is equal to the sum of the lengths of its sides. Therefore, the length of one side of the octagon is 104/8 = 13cm. ### Answer: 13 ``` This code is well-structured and easy to understand. However, there are some areas that could be improved. **Areas for improvement:** * **The code lacks documentation:** The code does not explain what the variables `Natalia` and `April` are, or what the purpose of the code is. * **The code uses unnecessary comments:** Some of the comments, such as `Reasoning: Natalia sold 48/2 =` are unnecessary. * **The code could be more concise:** Some of the code, such as `Natalia sold 48/2 =` could be combined with the following line: `Natalia sold 48/2 = 24 clips in May.` **Revised code:** Natalia sold clips to 48 of her friends in April, and then she sold half as many clips in May. How many clips did Natalia sell altogether in April and May? Reasoning: Natalia sold 48/2 = 24 clips in May. Natalia sold 48 + 24 = 72 clips altogether in April and May. ### Answer: 72 A regular octagon has a perimeter of 104cm. What is the length of one of its sides? Reasoning: The perimeter of an octagon is equal to the sum of the lengths of its sides. Therefore, the length of one side of the octagon is 104/8 = 13cm. ### Answer: 13
Expected answer: 13
Correct? Yes
Problem: A regular heptagon (7-sided polygon) has a perimeter of 637m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of a regular heptagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 637/7 = 91m. ### Answer: 91m
Expected answer: 91
Correct? Yes
Problem: A regular pentagon has a perimeter of 35m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of a regular pentagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 35m/5 = 7m. ### Answer: 7m
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?
Gemma 7B:
Reasoning: The perimeter is the sum of the lengths of the sides. We know the length of four sides, so we can find the length of the fifth side by subtracting the sum of the other side lengths from the perimeter. 45 + 93 + 36 + 22 = 206cm. 223 - 206 = 17cm. ### Answer: 17cm
Expected answer: 27
Correct? No
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?
Gemma 7B:
Reasoning: The perimeter is the sum of the lengths of all the sides of a polygon. Therefore, to find the length of the last unknown side, we need to subtract the sum of the other side lengths from the perimeter. The sum of the other side lengths is 75cm + 81cm + 22cm + 94cm + 91cm = 487cm. The length of the last unknown side is 423 - 487 = 36cm. ### Answer: 36 ``` This is an example of a mathematics teacher's solution to two problems. The teacher explains their reasoning clearly and formats their final answer correctly.
Expected answer: 50
Correct? No
Problem: A regular decagon (10-sided polygon) has a perimeter of 600m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of a decagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 600/10 = 60m. ### Answer: 60m
Expected answer: 60
Correct? Yes
Problem: The perimeter of a regular octagon is 632m. What is the length of each of its sides?
Gemma 7B:
**Reasoning:** The perimeter of a regular octagon is the sum of the lengths of its sides. Therefore, the length of each side is 632/8 = 79m. ### Answer: 79m
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?
Gemma 7B:
Reasoning: The perimeter of a regular septagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 161/7 = 23m. ### Answer: 23m
Expected answer: 23
Correct? Yes
Problem: A regular hexagon has a perimeter of 96m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of a regular hexagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 96/6 = 16m. ### Answer: 16m
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.
Gemma 7B:
Reasoning: The total perimeter of a nonagon is the sum of the length of its sides. Therefore, the total perimeter is 50m + 31m + 24m + 28m + 13m + 97m + 63m + 88m = 402m. The length of the ninth side is 402m - 48m = 354m. ### Answer: 354m
Expected answer: 8
Correct? No
Problem: A regular heptagon (7-sided polygon) has a perimeter of 385m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of a regular heptagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 385/7 = 55m. ### Answer: 55m
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?
Gemma 7B:
Reasoning: The total perimeter is the sum of the lengths of all the sides of a polygon. We know the total perimeter is 358 meters, and we know the lengths of the other sides. So, to find the length of the remaining side, we need to subtract the sum of the other side lengths from the total perimeter. 358 - (89 + 2 + 10 + 48 + 94) = 59 meters. ### Answer: 59 meters
Expected answer: 56
Correct? No
Problem: An octagon has a equal sides and its total perimeter is 496m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of an octagon is the sum of the length of its sides. Therefore, the length of each side is 496/8 = 62m. ### Answer: 62
Expected answer: 62
Correct? Yes
Problem: A regular octagon has a perimeter of 800m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of an octagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 800/8 = 100m. ### Answer: 100m
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?
Gemma 7B:
Reasoning: The perimeter of a nonagon is equal to the sum of the lengths of its sides. Therefore, the length of one side is 702/9 = 78 m. ### Answer: 78
Expected answer: 78
Correct? Yes
Problem: A regular nonagon has a perimeter of 855cm. What is the length of one side?
Gemma 7B:
Reasoning: The perimeter of a nonagon is equal to the sum of the lengths of its sides. Therefore, the length of one side is 855/9 = 95cm. ### Answer: 95
Expected answer: 95
Correct? Yes
Problem: If a regular heptagon has a perimeter of 504 meters, find the length of its side.
Gemma 7B:
Reasoning: The perimeter of a regular heptagon is equal to the sum of the lengths of its sides. Therefore, the length of one side of the heptagon is 504/7 = 72 meters. ### Answer: 72
Expected answer: 72
Correct? Yes
Problem: A regular nonagon has a perimeter of 657m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of a nonagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 657/9 = 73m. ### Answer: 73m
Expected answer: 73
Correct? Yes
Problem: Given a regular octagon where the total perimeter is 48 cm, what is the length of each side?
Gemma 7B:
Reasoning: The perimeter of an octagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 48/8 = 6 cm. ### Answer: 6
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?
Gemma 7B:
Reasoning: The total perimeter is the sum of the lengths of all the sides of a polygon. Therefore, to find the length of the remaining unknown side, we need to subtract the sum of the known side lengths from the total perimeter. The sum of the known side lengths is 28m + 37m + 51m + 84m + 54m + 31m + 94m = 411m. The remaining unknown side length is 399m - 411m = -12m. Since the length of a side cannot be negative, the length of the remaining unknown side is 0m. ### Answer: 0
Expected answer: 8
Correct? No
Problem: A regular nonagon has a perimeter of 342m. What is the length of one side?
Gemma 7B:
Reasoning: The perimeter of a nonagon is equal to the sum of the lengths of its sides. Therefore, the length of one side is 342/9 = 38m. ### Answer: 38m
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?
Gemma 7B:
Reasoning: The total perimeter is the sum of the length of all sides of a polygon. Therefore, the length of the eighth side is 330 - 7m - 59m - 49m - 38m - 53m - 21m - 34m = 10 m. ### Answer: 10 m
Expected answer: 69
Correct? No
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?
Gemma 7B:
Reasoning: The total perimeter of a decagon is the sum of the length of its side lengths. The total perimeter is 682m. The side lengths are 88m, 96m, 74m, 52m, 45m, 74m, 85m, 85m, and 43m. So, the total perimeter is 88m + 96m + 74m + 52m + 45m + 74m + 85m + 85m + 43m = 682m. ### Answer: 682
Expected answer: 40
Correct? No
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?
Gemma 7B:
Reasoning: The perimeter is the sum of the lengths of all the sides. Therefore, the length of each side is 161/7 = 23m. ### Answer: 23m
Expected answer: 23
Correct? Yes
Problem: A regular hexagon has a perimeter of 324m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of a regular hexagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 324/6 = 54m. ### Answer: 54
Expected answer: 54
Correct? Yes
Problem: A regular pentagon's perimeter is 385 meters. What is the length of one side?
Gemma 7B:
Reasoning: The perimeter of a regular pentagon is equal to the sum of the lengths of its sides. Therefore, the length of one side is 385/5 = 77 meters. ### Answer: 77
Expected answer: 77
Correct? Yes
Problem: A regular septagon (7-sided polygon) has a perimeter of 245m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of a regular septagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 245/7 = 35m. ### Answer: 35m
Expected answer: 35
Correct? Yes
Problem: A regular pentagon has a perimeter of 25cm. What is the length of one of its sides?
Gemma 7B:
Reasoning: The perimeter of a regular pentagon is equal to the sum of the lengths of its sides. Therefore, the length of one side of the pentagon is 25/5 = 5cm. ### Answer: 5
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.
Gemma 7B:
Reasoning: The total perimeter is the sum of the lengths of all the sides of a polygon. Therefore, the length of the sixth side is 380 - 9m - 49m - 100m - 73m - 84m = 30m. ### Answer: 30m
Expected answer: 65
Correct? No
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?
Gemma 7B:
Reasoning: The total perimeter is the sum of the lengths of all the sides of a polygon. Therefore, the missing side length is 419 - 23 - 67 - 57 - 94 - 93 - 18 - 30 = 12m. ### Answer: 12m
Expected answer: 37
Correct? No
Problem: A regular heptagon (7-sided polygon) has a perimeter of 287m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of a regular heptagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 287/7 = 41m. ### Answer: 41m
Expected answer: 41
Correct? Yes
Problem: A regular pentagon has a perimeter of 55m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of a regular pentagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 55/5 = 11m. ### Answer: 11m
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?
Gemma 7B:
Reasoning: The perimeter of a nonagon is equal to the sum of the length of its sides. Therefore, the length of each side is 657/9 = 73 meters. ### Answer: 73 **Note:** This is just an example of how I would solve the problem. You can replace the above text with your own problem and solution.
Expected answer: 73
Correct? Yes
Problem: A regular hexagon has a perimeter of 78m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of a regular hexagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 78/6 = 13m. ### Answer: 13m
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?
Gemma 7B:
Reasoning: The perimeter of an octagon is equal to the sum of the lengths of its sides. Therefore, the length of one side of the octagon is 600/8 = 75 meters. ### Answer: 75
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?
Gemma 7B:
Reasoning: The perimeter is the sum of the length of all the sides of a polygon. Therefore, the total length of the other sides is 356 - 17m = 339m. The remaining side length is 339m - 66m = 273m. ### Answer: 273
Expected answer: 75
Correct? No
Problem: A regular decagon has a perimeter of 930 cm. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of a decagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 930/10 = 93 cm. ### Answer: 93 ``` This code is well-structured and easy to understand. However, there are some areas that could be improved. **Areas for improvement:** * **The code lacks documentation:** The code does not explain what the variables `Natalia` and `April` are, or what the purpose of the code is. * **The code could be more concise:** Some of the lines could be combined or shortened to make the code more concise. * **The code could be more modular:** The code could be divided into smaller functions to make it more modular and easier to read. **Overall, this code is a good example of clear and concise mathematics problem-solving.** **Here is the improved code:** Natalia sold clips to 48 of her friends in April, and then she sold half as many clips in May. How many clips did Natalia sell altogether in April and May? Reasoning: Natalia sold 48/2 = 24 clips in May. Natalia sold 48 + 24 = 72 clips altogether in April and May. ### Answer: 72 A regular decagon has a perimeter of 930 cm. What is the length of each side? Reasoning: The perimeter of a decagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 930 / 10 = 93 cm. ### Answer: 93
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?
Gemma 7B:
Reasoning: The total perimeter is the sum of the length of all the sides of a polygon. Therefore, the total perimeter is 24m + 25m + 75m + 38m + 18m + 42m + 61m = 359m. Since the total perimeter is 359m, and the other sides are already known, the unknown side must be 359m - (24m + 25m + 75m + 38m + 18m + 42m + 61m) = 0m. ### Answer: 0m
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?
Gemma 7B:
Reasoning: The total perimeter is the sum of the length of all the side lengths. Therefore, the total perimeter is 52+52+44+53+41+91+25+2 = 368m. The final side length is 2m. ### Answer: 2m
Expected answer: 8
Correct? No
Problem: A regular octagon has a perimeter of 592cm. What is the length of one side?
Gemma 7B:
Reasoning: The perimeter of an octagon is equal to the sum of the lengths of its sides. Therefore, the length of one side is 592/8 = 74cm. ### Answer: 74
Expected answer: 74
Correct? Yes
Problem: A regular heptagon has a perimeter of 245m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of a regular heptagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 245/7 = 35m. ### Answer: 35m
Expected answer: 35
Correct? Yes
Problem: A regular decagon has a perimeter of 140m. What is the length of each side?
Gemma 7B:
Reasoning: The perimeter of a decagon is equal to the sum of the lengths of its sides. Therefore, the length of each side is 140/10 = 14m. ### Answer: 14m
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?
Gemma 7B:
Reasoning: The total perimeter is the sum of the length of all the sides of a polygon. Therefore, the total perimeter is 44+5+96+78+49+84+72+74+21+39 = 655cm. The length of the 11th side is not given in the text, therefore I cannot answer this question. ### Answer: I cannot answer this question.
Expected answer: 93
Correct? No
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?
Gemma 7B:
Reasoning: The total perimeter is the sum of the lengths of all the sides of a polygon. Therefore, the length of the remaining side is 265 - 69 - 81 - 34 - 35 - 38 = 36m. ### Answer: 36m
Expected answer: 8
Correct? No
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.
Gemma 7B:
Reasoning: The perimeter of a pentagon is the sum of the length of its side lengths. Therefore, the total perimeter is 22m + 14m + 93m + 75m + x = 234m. Substituting the known values into the equation, we get 22m + 14m + 93m + 75m + x = 234m. Solving for x, we get x = 234m - 22m - 14m - 93m - 75m = 12m. ### Answer: 12m
Expected answer: 30
Correct? No