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?

Gemini-1.5 Flash:

Reasoning: The sum of the given measurements is 41 + 28 + 90 + 32 + 10 + 98 = <<41+28+90+32+10+98=299>>299 miles.
The remaining measurement is 368 - 299 = <<368-299=69>>69 miles.
### 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?

Gemini-1.5 Flash:

Reasoning: We know the sum of the lengths of the four sides is 70+36+53+45 = 204 cm. 
Since the total perimeter of the pentagon is 300 cm, the length of the fifth side is 300 - 204 = 96 cm.

### 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?

Gemini-1.5 Flash:

We can find the length of the ninth side by subtracting the sum of the lengths of the other eight sides from the total perimeter.

The sum of the lengths of the other eight sides is 14cm + 94cm + 3cm + 20cm + 57cm + 83cm + 96cm + 85cm = 452cm.

Therefore, the length of the ninth side is 521cm - 452cm = 69cm.

### Answer: 69cm 

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?

Gemini-1.5 Flash:

Reasoning: To find the length of the sixth side, we need to subtract the sum of the lengths of the first five sides from the total perimeter. 
The sum of the first five sides is 54cm + 51cm + 5cm + 22cm + 93cm = <<54+51+5+22+93=225>>225cm.
The length of the sixth side is 274cm - 225cm = <<274-225=49>>49cm.

### Answer: 49cm 

Expected answer: 49

Correct? Yes

Problem: A regular pentagon has a perimeter of 310 m. What is the length of each side?

Gemini-1.5 Flash:

Reasoning: A regular pentagon has 5 equal sides. Therefore, the length of each side is 310 m / 5 = 62 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?

Gemini-1.5 Flash:

Reasoning: We can find the sum of the known sides by adding: 78 + 93 + 21 + 4 + 21 = <<78+93+21+4+21=217>>217 cm.  The length of the last side can be found by subtracting the sum of the known sides from the total perimeter: 315 - 217 = <<315-217=98>> 98 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?

Gemini-1.5 Flash:

Reasoning: An octagon has 8 sides, and the perimeter is the total length of all the sides.  To find the length of one side, we divide the perimeter by the number of sides. 

So, the length of each side is 160m / 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?

Gemini-1.5 Flash:

Here's how to solve this problem:

1. **Add up the known side lengths:** 6 + 4 + 95 + 34 + 19 + 14 + 26 = 208 cm

2. **Subtract the sum of the known side lengths from the total perimeter:** 224 cm - 208 cm = 16 cm

**Therefore, the length of the other side is 16 cm.** 
### Answer: 16 cm 

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?

Gemini-1.5 Flash:

Reasoning: A regular hexagon has 6 equal sides. To find the length of one side, we divide the perimeter by the number of sides: 174 meters / 6 sides = 29 meters/side.

### 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?

Gemini-1.5 Flash:

To find the length of the 11th side, we can subtract the sum of the known side lengths from the total perimeter.

Here's the calculation:

1. Sum of known side lengths: 65cm + 22cm + 32cm + 31cm + 78cm + 88cm + 7cm + 29cm + 36cm + 54cm = 442cm

2. Length of the 11th side: 538cm - 442cm = 96cm

### Answer: 96cm 

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?

Gemini-1.5 Flash:

Reasoning: We need to find the sum of the five known side lengths: 61 + 84 + 80 + 11 + 71 = <<61+84+80+11+71=307>> 307 cm.
To find the length of the last side, we need to subtract this sum from the desired total length: 357 - 307 = <<357-307=50>> 50 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?

Gemini-1.5 Flash:

Reasoning: A regular octagon has 8 equal sides.  To find the length of one side, we divide the perimeter by the number of sides: 544m / 8 = 68m.
### Answer: 68m 

Expected answer: 68

Correct? Yes

Problem: The perimeter of a regular decagon (10-sided polygon) is 960m. Find the length of one side.

Gemini-1.5 Flash:

Reasoning: A regular decagon has 10 sides of equal length.  The perimeter is the total length of all the sides. Therefore, to find the length of one side, we divide the perimeter by the number of sides:

Length of one side = Perimeter / Number of sides = 960m / 10 = 96m

### Answer: 96m 

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?

Gemini-1.5 Flash:

Reasoning: A regular heptagon has 7 equal sides.  Therefore, to find the length of one side, we divide the total perimeter by 7. 

203m / 7 = 29m

### Answer: 29m 

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?

Gemini-1.5 Flash:

Reasoning: Since a regular heptagon has 7 equal sides, we can find the length of each side by dividing the perimeter by 7.

The length of each side is 49 meters / 7 = 7 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?

Gemini-1.5 Flash:

Reasoning: A regular heptagon has 7 sides of equal length.  To find the length of one side, we divide the perimeter by the number of sides: 329m / 7 = 47m.
### Answer: 47m 

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?

Gemini-1.5 Flash:

Reasoning: First, we find the sum of the given side lengths: 86m + 80m + 47m + 93m + 99m = 405m.
Then, we subtract this sum from the total perimeter to find the length of the sixth side: 486m - 405m = 81m.

### Answer: 81m 

Expected answer: 81

Correct? Yes

Problem: A regular heptagon has a perimeter of 546m. What is the length of each side?

Gemini-1.5 Flash:

Reasoning: A regular heptagon has 7 sides of equal length. To find the length of each side, we divide the perimeter by the number of sides: 546m / 7 sides = 78m/side.

### 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?

Gemini-1.5 Flash:

Reasoning:  The sum of the lengths of the first eight sides is 26 + 45 + 75 + 68 + 63 + 80 + 100 = 457 cm.
The ninth side is the difference between the perimeter and the sum of the lengths of the first eight sides, which is 532 - 457 = 75 cm.

### Answer: 75 cm 

Expected answer: 75

Correct? Yes

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?

Gemini-1.5 Flash:

Reasoning: First, add all the known sides: 62m + 76m + 98m + 74m + 54m + 4m + 24m + 48m = 440m
Then subtract that sum from the total perimeter to find the length of the unknown side: 452m - 440m = 12m
### Answer: 12m 

Expected answer: 12

Correct? Yes

Problem: A regular hexagon has a perimeter of 78m. What is the length of each side?

Gemini-1.5 Flash:

Reasoning: A regular hexagon has 6 equal sides.
To find the length of each side, we divide the perimeter by the number of sides: 78m / 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?

Gemini-1.5 Flash:

Reasoning: A nonagon has 9 sides.  To find the length of each side, we divide the perimeter by the number of sides: 171m / 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?

Gemini-1.5 Flash:

Reasoning: We first add up the known side lengths: 8 + 17 + 30 + 17 + 86 + 55 + 68 = 281 cm. 
Then, we subtract that sum from the total perimeter to find the unknown side length: 318 - 281 = 37 cm.

### 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?

Gemini-1.5 Flash:

Reasoning: The perimeter of a polygon is the total length of all its sides.  Since the polygon is regular, all sides are equal in length.  Therefore, to find the length of each side, we divide the perimeter by the number of sides. 

The length of each side is 858m / 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?

Gemini-1.5 Flash:

Reasoning: A decagon has 10 sides.  Therefore, the length of each side is 360m / 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?

Gemini-1.5 Flash:

A regular hexagon has 6 equal sides. 

To find the length of each side, we divide the perimeter by the number of sides:

522m / 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.

Gemini-1.5 Flash:

Reasoning: To find the length of each side, we need to divide the total perimeter by the number of sides. 

The perimeter is 418 meters and there are 11 sides, so each side has a length of 418/11 = 38 meters. 

### 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?

Gemini-1.5 Flash:

Reasoning: To find the length of the sixth side, we need to subtract the sum of the known sides from the total perimeter. 

The sum of the known sides is 56m + 73m + 39m + 24m + 26m = 218m

Therefore, the length of the sixth side is 278m - 218m = 60m.

### Answer: 60m 

Expected answer: 60

Correct? Yes

Problem: A regular pentagon has a perimeter of 385cm. How long is each side?

Gemini-1.5 Flash:

Reasoning: A regular pentagon has five sides of equal length. Therefore, to find the length of each side, we divide the perimeter by 5. 
 
The length of each side is 385 cm / 5 = 77 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?

Gemini-1.5 Flash:

Reasoning: First, we need to sum the lengths of the ten known sides: 97m + 93m + 35m + 1m + 27m + 86m + 68m + 96m + 45m + 61m = 619m.
Next, we subtract the sum of the ten known sides from the perimeter of the polygon to find the length of the eleventh side: 663m - 619m = 44m. 

### Answer: 44m

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?

Gemini-1.5 Flash:

Reasoning:  We know the sum of the lengths of the first nine sides is 54+49+85+48+85+19+94+44+54 = 432m. To find the length of the tenth side, we subtract the sum of the lengths of the first nine sides from the total perimeter: 575m - 432m = 143m.

### Answer: 143m 

Expected answer: 43

Correct? No

Problem: Given a regular octagon with a perimeter of 248m, what is the length of each side?

Gemini-1.5 Flash:

A regular octagon has 8 equal sides. To find the length of each side, we divide the perimeter by the number of sides:

Length of each side = Perimeter / Number of sides

Length of each side = 248m / 8

Length of each side = 31m

### Answer: 31m 

Expected answer: 31

Correct? Yes

Problem: A regular pentagon has a perimeter of 390m. What is the length of each side?

Gemini-1.5 Flash:

Reasoning: A regular pentagon has 5 equal sides.  To find the length of each side, we divide the perimeter by 5. 
### 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.

Gemini-1.5 Flash:

Reasoning: To find the length of the tenth side, we need to subtract the sum of the nine given side lengths from the total perimeter. 

Let's calculate the sum of the nine given side lengths: 6m + 85m + 83m + 73m + 25m + 66m + 54m + 87m + 21m = 490m

Now, subtract this sum from the total perimeter: 522m - 490m = 32m

Therefore, the length of the tenth side is 32m.

### Answer: 32m 

Expected answer: 22

Correct? No

Problem: A regular octagon has a perimeter of 408m. What is the length of each side?

Gemini-1.5 Flash:

Reasoning: A regular octagon has 8 equal sides.  To find the length of each side, we divide the perimeter by the number of sides: 408m / 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?

Gemini-1.5 Flash:

Reasoning: An octagon has 8 sides. Therefore, the length of each side is 696m / 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?

Gemini-1.5 Flash:

Reasoning: An octagon has 8 sides. If the perimeter is 744m, and all sides are equal, then each side is 744m / 8 = <<744/8=93>>93m long.
### Answer: 93m 

Expected answer: 93

Correct? Yes

Problem: A regular nonagon (9-sided polygon) has a perimeter of 270m. What is the length of one side?

Gemini-1.5 Flash:

Reasoning: A regular polygon has all sides equal.  Therefore, to find the length of one side, we divide the perimeter by the number of sides: 270m / 9 sides = 30m/side.
### 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?

Gemini-1.5 Flash:

Reasoning: To find the length of the unknown side, we need to subtract the sum of the known sides from the total perimeter.

First, we add up the lengths of the eight known sides: 30cm + 18cm + 68cm + 23cm + 72cm + 57cm + 33cm + 19cm = 320cm

Then, we subtract this sum from the total perimeter: 350cm - 320cm = 30cm

Therefore, the length of the unknown ninth side is 30cm.

### Answer: 30cm 

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?

Gemini-1.5 Flash:

Reasoning: To find the length of the ninth side, we need to sum up the lengths of the known sides and subtract the result from the total perimeter.  

The sum of the known sides is 19m + 7m + 10m + 16m + 32m + 15m + 70m = 179m.

Subtracting this sum from the total perimeter, we get 188m - 179m = 9m.

### Answer: 9m 

Expected answer: 19

Correct? No

Problem: A regular hexagon has a perimeter of 90m. What is the length of each side?

Gemini-1.5 Flash:

Reasoning: A regular hexagon has 6 equal sides. To find the length of each side, we divide the perimeter by the number of sides.

So, the length of each side is 90m / 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?

Gemini-1.5 Flash:

Reasoning:  A regular heptagon has 7 equal sides.  To find the length of one side, we divide the total perimeter by the number of sides: 287 meters / 7 sides = 41 meters/side.

### Answer: 41 meters 

Expected answer: 41

Correct? Yes

Problem: A regular pentagon has a perimeter of 50m. What is the length of each side?

Gemini-1.5 Flash:

Reasoning: A regular pentagon has five equal sides.  The perimeter is the total length of all the sides.  Therefore, to find the length of one side, we divide the perimeter by the number of sides.
 
  50m / 5 sides = 10m/side

### Answer: 10m 

Expected answer: 10

Correct? Yes

Problem: A regular nonagon has a perimeter of 63m. What is the length of each side?

Gemini-1.5 Flash:

Reasoning: A nonagon has 9 sides.  To find the length of each side, we divide the perimeter by the number of sides: 63m / 9 sides = 7m/side. 
### 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?

Gemini-1.5 Flash:

Reasoning:  A regular hexagon has 6 equal sides. To find the length of one side, we divide the perimeter by the number of sides.

The length of one side is 354m / 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?

Gemini-1.5 Flash:

Reasoning: To find the length of the last side, we need to subtract the sum of the known sides from the total perimeter. 
The sum of the known sides is 59 + 16 + 15 + 35 + 89 + 16 + 43 + 7 = 276 meters.
Therefore, the length of the last unknown side is 286 - 276 = 10 meters.

### Answer: 10 meters 

Expected answer: 6

Correct? No

Problem: A regular heptagon (7-sided polygon) has a perimeter of 616m. What is the length of each side?

Gemini-1.5 Flash:

Reasoning: Since a regular heptagon has 7 equal sides, we can find the length of one side by dividing the total perimeter by 7. 

616 meters / 7 sides = 88 meters/side

### Answer: 88 meters 

Expected answer: 88

Correct? Yes

Problem: A regular hexagon has a perimeter of 36m. What is the length of each side?

Gemini-1.5 Flash:

A regular hexagon has 6 equal sides. 
Therefore, the length of each side is the perimeter divided by the number of sides: 36m / 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?

Gemini-1.5 Flash:

Reasoning: To find the length of the twelfth side, we need to subtract the sum of the lengths of the first 11 sides from the total perimeter.

First, we sum the lengths of the 11 measured sides: 88 + 24 + 83 + 64 + 16 + 14 + 90 + 36 + 47 = 462 cm

Then, we subtract this sum from the total perimeter to find the length of the twelfth side: 492 cm - 462 cm = 30 cm

### Answer: 30 cm 

Expected answer: 30

Correct? Yes

Problem: A regular hexagon has a perimeter of 306m. What is the length of each side?

Gemini-1.5 Flash:

A regular hexagon has 6 equal sides. To find the length of one side, we can divide the perimeter by 6.

The length of each side is 306m / 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?

Gemini-1.5 Flash:

Reasoning:  A regular heptagon has 7 equal sides. To find the length of one side, we divide the total perimeter by the number of sides.

Calculation: 238 meters / 7 sides = 34 meters/side

### 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?

Gemini-1.5 Flash:

Reasoning: A regular hexagon has 6 equal sides.  To find the length of one side, we divide the total perimeter by the number of sides: 42m / 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?

Gemini-1.5 Flash:

Reasoning: A regular octagon has 8 equal sides.  
To find the length of one side, we divide the perimeter by the number of sides: 624m / 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?

Gemini-1.5 Flash:

Reasoning: To find the length of the tenth side, we need to subtract the sum of the lengths of the first nine sides from the total perimeter. 
The sum of the lengths of the first nine sides is 17+13+61+16+11+83+28+48+93 = 369 meters.
Subtracting this sum from the total perimeter, we get 468-369 = 99 meters.

### Answer: 99 

Expected answer: 98

Correct? No

Problem: A regular pentagon has a perimeter of 380m. What is the length of each side?

Gemini-1.5 Flash:

Reasoning: A regular pentagon has 5 equal sides. To find the length of one side, we divide the perimeter by the number of sides: 380m / 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?

Gemini-1.5 Flash:

Reasoning: A regular octagon has 8 sides of equal length.  To find the length of one side, we divide the perimeter by the number of sides: 104cm / 8 sides = 13cm/side.

### Answer: 13cm 

Expected answer: 13

Correct? Yes

Problem: A regular heptagon (7-sided polygon) has a perimeter of 637m. What is the length of each side?

Gemini-1.5 Flash:

Reasoning: Since a regular heptagon has 7 equal sides, we can find the length of each side by dividing the perimeter by 7.

Calculation: 637m / 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?

Gemini-1.5 Flash:

Reasoning: A regular pentagon has five equal sides.  Therefore, the length of each side is the perimeter divided by 5.  
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?

Gemini-1.5 Flash:

Reasoning: The perimeter of a shape is the total length of all its sides. So, to find the length of the fifth side, we need to subtract the lengths of the other four sides from the total perimeter. 
 
The sum of the lengths of the four known sides is 45cm + 93cm + 36cm + 22cm = <<45+93+36+22=196>>196cm.
 
Therefore, the length of the fifth side is 223cm - 196cm = <<223-196=27>>27cm.

### Answer: 27cm

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?

Gemini-1.5 Flash:

Reasoning: We can find the sum of the known sides: 75cm + 81cm + 22cm + 94cm + 91cm + 10cm = 373cm. 
To find the length of the last side, we can subtract the sum of the known sides from the total perimeter: 423cm - 373cm = 50cm.

### Answer: 50cm 

Expected answer: 50

Correct? Yes

Problem: A regular decagon (10-sided polygon) has a perimeter of 600m. What is the length of each side?

Gemini-1.5 Flash:

Reasoning:  A regular decagon has 10 equal sides. To find the length of one side, we divide the perimeter by the number of sides. 

Therefore, the length of each side is 600m / 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?

Gemini-1.5 Flash:

Reasoning: An octagon has 8 sides. The perimeter is the total length of all the sides, so we divide the total perimeter by the number of sides to get the length of one side. 
632 m / 8 = <<632/8=79>> 79 meters

### 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?

Gemini-1.5 Flash:

Reasoning:  A regular polygon has all sides equal. To find the length of one side, we divide the total perimeter by the number of sides. 

Therefore, each side of the septagon is 161m / 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?

Gemini-1.5 Flash:

A regular hexagon has 6 equal sides.  
Therefore, the length of each side is 96m / 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.

Gemini-1.5 Flash:

Reasoning: We know that the perimeter of a polygon is the sum of the lengths of all its sides.  We can find the length of the ninth side by subtracting the sum of the lengths of the other eight sides from the total perimeter. 

The sum of the lengths of the first eight sides is 50m + 31m + 24m + 28m + 13m + 97m + 63m + 88m = 394m.

The length of the ninth side is 402m - 394m = 8m.

### Answer: 8m 

Expected answer: 8

Correct? Yes

Problem: A regular heptagon (7-sided polygon) has a perimeter of 385m. What is the length of each side?

Gemini-1.5 Flash:

Reasoning: Since a heptagon has 7 sides, and the perimeter is the total length of all sides, we can find the length of each side by dividing the perimeter by the number of sides.

Length of each side = Perimeter / Number of sides = 385m / 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?

Gemini-1.5 Flash:

Reasoning: The total length of the five sides we know is 89 + 2 + 10 + 48 + 94 = 243 meters.
The total length of all the sides except the last one is 243 + 59 = 302 meters.
The length of the remaining side is 358 - 302 = 56 meters.
### 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?

Gemini-1.5 Flash:

Reasoning: An octagon has 8 sides. 
The length of each side is 496m/8 = <<496/8=62>>62m.

### Answer: 62m

Expected answer: 62

Correct? Yes

Problem: A regular octagon has a perimeter of 800m. What is the length of each side?

Gemini-1.5 Flash:

Reasoning: A regular octagon has 8 equal sides. 
Therefore, the length of each side is 800m / 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?

Gemini-1.5 Flash:

A nonagon has 9 sides.  Since the perimeter is the total length of all the sides, we can find the length of one side by dividing the perimeter by the number of sides. 

Therefore, the length of one side is 702 m / 9 = 78 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?

Gemini-1.5 Flash:

A nonagon has 9 sides.  To find the length of one side, we divide the perimeter by the number of sides. 

855 cm / 9 sides = 95 cm/side

### 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.

Gemini-1.5 Flash:

Reasoning: A regular heptagon has 7 sides of equal length.  
If the perimeter is 504 meters, then each side is 504/7 = <<504/7=72>> meters long. 
### Answer: 72 meters 

Expected answer: 72

Correct? Yes

Problem: A regular nonagon has a perimeter of 657m. What is the length of each side?

Gemini-1.5 Flash:

A nonagon has 9 sides.  To find the length of each side, we divide the perimeter by the number of sides:

657m / 9 sides = 73m/side

### 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?

Gemini-1.5 Flash:

Reasoning: A regular octagon has 8 equal sides.  If the total perimeter is 48 cm, then each side is 48 cm / 8 = 6 cm long.

### 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?

Gemini-1.5 Flash:

Reasoning: We know the sum of the known sides is 28m + 37m + 51m + 84m + 54m + 31m + 94m + 12m = 391m.  We also know the total perimeter is 399m.  Therefore, the remaining unknown side is 399m - 391m = 8m long.

### Answer: 8m 

Expected answer: 8

Correct? Yes

Problem: A regular nonagon has a perimeter of 342m. What is the length of one side?

Gemini-1.5 Flash:

A nonagon has 9 sides.  To find the length of one side, we divide the perimeter by the number of sides.  

The length of one side is 342m / 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?

Gemini-1.5 Flash:

Reasoning: To find the length of the eighth side, we first need to calculate the sum of the lengths of the first seven sides: 7m + 59m + 49m + 38m + 53m + 21m + 34m = 261m.
Then, we subtract this sum from the total perimeter to find the length of the eighth side: 330m - 261m = 69m. 
### Answer: 69 m 

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?

Gemini-1.5 Flash:

Reasoning:  To find the length of the tenth side, we need to subtract the sum of the known sides from the total perimeter. 

First, let's add up the lengths of the nine known sides: 88m + 96m + 74m + 52m + 45m + 74m + 85m + 85m + 43m = 642m

Now, we subtract this sum from the total perimeter: 682m - 642m = 40m

Therefore, the length of the tenth side is 40m.

### Answer: 40m 

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?

Gemini-1.5 Flash:

Reasoning: A regular septagon has 7 equal sides.  To find the length of each side, we divide the total perimeter by the number of sides: 161m / 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?

Gemini-1.5 Flash:

Reasoning: A regular hexagon has 6 equal sides.  To find the length of one side, we divide the perimeter by the number of sides: 324m / 6 = 54m.

### Answer: 54m 

Expected answer: 54

Correct? Yes

Problem: A regular pentagon's perimeter is 385 meters. What is the length of one side?

Gemini-1.5 Flash:

Reasoning: A regular pentagon has 5 equal sides. 
The length of one side of the pentagon is 385/5 = <<385/5=77>>77 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?

Gemini-1.5 Flash:

Reasoning:  A regular septagon has 7 equal sides.  To find the length of one side, we divide the total perimeter by the number of sides.

Therefore, the length of each side is 245m / 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?

Gemini-1.5 Flash:

A regular pentagon has 5 equal sides. 
To find the length of one side, we divide the perimeter by the number of sides: 25 cm / 5 sides = 5 cm/side.

### 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.

Gemini-1.5 Flash:

Here's how to solve the problem:

1. **Add up the known sides:** 9m + 49m + 100m + 73m + 84m = 315m

2. **Subtract the sum of the known sides from the total perimeter:** 380m - 315m = 65m

**Therefore, the length of the sixth side is 65m.** 

### 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?

Gemini-1.5 Flash:

Reasoning: To find the length of the missing side, we can subtract the sum of the lengths of the known sides from the total perimeter. 
The sum of the lengths of the known sides is 23 + 67 + 57 + 94 + 93 + 18 + 30 = 382m.
Therefore, the length of the missing side is 419m - 382m = <<419-382=37>>37m.
### 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?

Gemini-1.5 Flash:

Reasoning:  A regular heptagon has 7 sides of equal length. To find the length of one side, we divide the total perimeter by the number of sides.

So, the length of each side is 287m / 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?

Gemini-1.5 Flash:

Reasoning: A regular pentagon has 5 equal sides.
The length of each side is 55m / 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?

Gemini-1.5 Flash:

Reasoning: Since a nonagon has nine sides, and the perimeter is 657 meters, each side is 657/9 = 73 meters long.
### Answer: 73 meters 

Expected answer: 73

Correct? Yes

Problem: A regular hexagon has a perimeter of 78m. What is the length of each side?

Gemini-1.5 Flash:

Reasoning: A regular hexagon has 6 equal sides.  To find the length of one side, we divide the perimeter by the number of sides: 78m / 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?

Gemini-1.5 Flash:

Reasoning: A regular octagon has 8 equal sides. 
To find the length of one side, we divide the total perimeter by the number of sides: 600 meters / 8 sides = 75 meters per side.

### 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?

Gemini-1.5 Flash:

Reasoning: We first need to add up the lengths of the sides we know: 39m + 26m + 47m + 52m + 66m + 17m + 34m = 281m.
Then, we subtract that sum from the total perimeter to find the length of the last side: 356m - 281m = 75m.

### Answer: 75m 

Expected answer: 75

Correct? Yes

Problem: A regular decagon has a perimeter of 930 cm. What is the length of each side?

Gemini-1.5 Flash:

Reasoning: A decagon has 10 sides.  Therefore, to find the length of each side, we divide the perimeter by 10.

930 cm / 10 = 93 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?

Gemini-1.5 Flash:

Reasoning: 
1. We know the decagon has 10 sides.
2. We are given the lengths of 7 sides.
3. We know the total perimeter is 359m.
4. We can find the sum of the known sides: 24m + 25m + 75m + 38m + 18m + 42m + 61m = 283m
5. Subtract the sum of the known sides from the total perimeter to find the combined length of the remaining 3 sides: 359m - 283m = 76m
6. Since the remaining 3 sides must have a total length of 76m, each side must be 76m / 3 = 25.33m (approximately). 

### Answer: 25.33m (approximately) 

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?

Gemini-1.5 Flash:

Reasoning: To find the length of the final side, we subtract the sum of the known side lengths from the total perimeter. The sum of the known side lengths is 52m + 52m + 44m + 53m + 41m + 91m + 25m + 2m = 360m.  The difference between the total perimeter and the sum of the known side lengths is 368m - 360m = 8m.

### Answer: 8m 

Expected answer: 8

Correct? Yes

Problem: A regular octagon has a perimeter of 592cm. What is the length of one side?

Gemini-1.5 Flash:

Reasoning: A regular octagon has 8 equal sides.
The length of one side is 592cm/8 = <<592/8=74>>74 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?

Gemini-1.5 Flash:

A regular heptagon has 7 sides of equal length. 
To find the length of each side, we divide the perimeter by the number of sides: 245m / 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?

Gemini-1.5 Flash:

Reasoning: A decagon has 10 sides.  To find the length of each side, we divide the perimeter by the number of sides. 
 
The length of each side is 140m / 10 = <<140/10=14>>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?

Gemini-1.5 Flash:

Reasoning:  We know the sum of the lengths of the first 10 sides is 44 + 5 + 96 + 78 + 49 + 84 + 72 + 74 + 21 + 39 = 562 cm.
The total perimeter of the polygon is 655 cm, so the length of the 11th side is 655 - 562 = 93 cm.

### 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?

Gemini-1.5 Flash:

Reasoning: The sum of the given sides is 69m + 81m + 34m + 35m + 38m = 257m. 
To find the length of the remaining side, subtract the sum of the given sides from the total perimeter: 265m - 257m = 8m.
### Answer: 8m 

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.

Gemini-1.5 Flash:

Reasoning: We know that the perimeter of a polygon is the sum of all its sides.
We are given that the total perimeter is 234m, and we know the lengths of four sides: 22m, 14m, 93m, and 75m. 
Therefore, the length of the fifth side is equal to the total perimeter minus the sum of the lengths of the four known sides.
So, the length of the fifth side is 234m - (22m + 14m + 93m + 75m) = 234m - 204m.
### Answer: 30m 

Expected answer: 30

Correct? Yes