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 Pro:

Reasoning: Let's add up the provided measurements: 41 + 28 + 90 + 32 + 10 + 98 = 299 miles
Now, let's subtract the sum of the known measurements from the total measurement: 368 - 299 = 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 Pro:

Reasoning: A regular pentagon has 5 sides of equal length.  Since the perimeter is the sum of all sides, and we know the lengths of 4 sides and the total perimeter, we can determine the length of the fifth side.

First, find the combined length of the known sides: 70cm + 36cm + 53cm + 45cm = 204cm.

Then, subtract the combined length of the known sides from the total perimeter to find the length of the fifth side: 300cm - 204cm = 96cm.

However, this answer doesn't make sense because a regular pentagon has all sides equal, and 96cm is significantly different from the other side lengths. Therefore, there's an error in the problem statement, and it's not possible to have a regular pentagon with those side lengths.

### Answer: Not a regular pentagon. 

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?

Gemini-1.5 Pro:

Reasoning: A regular nonagon has 9 sides of equal length.  Since the perimeter of the nonagon is 521cm, each side has length 521/9 = <<521/9=57.89>>57.89cm.
### Answer: 57.89cm 

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?

Gemini-1.5 Pro:

Reasoning: The total length of the five sides is 54 cm + 51 cm + 5 cm + 22 cm + 93 cm = 225 cm.
The sixth side has a length of 274 cm - 225 cm = 49 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?

Gemini-1.5 Pro:

Reasoning: A pentagon has 5 sides. 
The length of each side is 310/5 = <<310/5=62>>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 Pro:

Reasoning: The total length of the given 5 sides is 78 cm + 93 cm + 21 cm + 4 cm + 21 cm = 217 cm.
Subtracting the length of the given 5 sides from the total perimeter gives us 315 cm - 217 cm = 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 Pro:

Reasoning: An octagon has 8 sides of equal length. 
To find the length of each side, divide the total perimeter by the number of sides: 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 Pro:

Reasoning: The sum of the lengths of the seven sides is 6 + 4 + 95 + 34 + 19 + 14 + 26 = 198 cm.
The length of the other side is 224 - 198 = 26 cm. 
### 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?

Gemini-1.5 Pro:

Reasoning: A hexagon has 6 sides.  Since the hexagon is regular, all the sides are equal.  Therefore, one side has length 174/6 = <<174/6=29>>29 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?

Gemini-1.5 Pro:

Reasoning: Let 'x' be the length of the 11th side. We know the total perimeter is 538cm, so the sum of all sides equals the perimeter.
65 + 22 + 32 + 31 + 78 + 88 + 7 + 29 + 36 + 54 + x + 1 = 538
Combining the known side lengths: 433 + x = 538
To find x, subtract 433 from both sides: x = 538 - 433 = 105
Therefore, the length of the 11th side is 105cm. 
### Answer: 105cm 

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?

Gemini-1.5 Pro:

Reasoning: The sum of the lengths of the first five sides of the hexagon is 61 cm + 84 cm + 80 cm + 11 cm + 71 cm = 307 cm.
The length of the last side should be 357 cm - 307 cm = 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 Pro:

Reasoning: An octagon has 8 sides.
The length of one side is 544/8 = <<544/8=68>>68 m.
### Answer: 68 m 

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 Pro:

Reasoning:  A regular decagon has 10 equal sides. To find the length of one side, divide the total perimeter by the number of sides: 960 m / 10 = 96 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?

Gemini-1.5 Pro:

Reasoning: A heptagon has 7 equal sides. To find the length of one side, divide the total perimeter by the number of sides: 203m / 7 = <<203/7=29>>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 Pro:

Reasoning: A heptagon has 7 sides, and the perimeter is the total length of all the sides.  Therefore, the length of each side is the perimeter divided by the number of sides. 
So, each side of the heptagon is 49 meters / 7 sides = <<49/7=7>>7 meters long.
### 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 Pro:

Reasoning: A heptagon has 7 sides. Since it is a regular heptagon, all sides are equal.
The length of each side is 329/7 = <<329/7=47>>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 Pro:

Reasoning: The total length of the given five sides of the heptagon is 86m + 80m + 47m + 93m + 99m = 405m.
The total length of the missing two sides is 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 Pro:

Reasoning: A heptagon has 7 sides. The length of each side is 546/7 = <<546/7=78>>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?

Gemini-1.5 Pro:

Reasoning:  The total length of the known sides is 26+45+75+68+63+80+100 = <<26+45+75+68+63+80+100=457>>457 cm.
The length of the ninth side is 532-457 = <<532-457=75>>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 Pro:

Reasoning: A decagon has 10 sides. The total length of the given 9 sides of the decagon is 62m + 76m + 98m + 74m + 54m + 4m + 24m + 48m = 440m
The length of the unknown side is 452m - 440m = 12m.
Since all sides of a decagon are equal in length, the length of each side of the decagon is 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 Pro:

Reasoning: A hexagon has 6 sides. So, the length of each side is 78/6 = <<78/6=13>>13 m.
### Answer: 13 m 

Expected answer: 13

Correct? Yes

Problem: A regular nonagon has a perimeter of 171m. What is the length of each side?

Gemini-1.5 Pro:

Reasoning: A nonagon has 9 sides. The length of each side is 171/9 = <<171/9=19>>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 Pro:

Reasoning: 
First, sum up the known side lengths: 8 cm + 17 cm + 30 cm + 17 cm + 86 cm + 55 cm + 68 cm = 281 cm. 
Then, subtract the sum of the known side lengths from the total perimeter to find the length of the unknown side: 318 cm - 281 cm = 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 Pro:

Reasoning:  An 11-sided polygon has 11 sides. Since it is a regular polygon, all sides are equal.
The length of each side is 858/11 = <<858/11=78>>78 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?

Gemini-1.5 Pro:

Reasoning: A regular decagon has 10 equal sides. 
The length of each side is 360/10 = <<360/10=36>>36 m. 
### Answer: 36 m

Expected answer: 36

Correct? Yes

Problem: A regular hexagon has a perimeter of 522m. What is the length of each side?

Gemini-1.5 Pro:

Reasoning: A hexagon has 6 sides. The length of each side is 522/6 = <<522/6=87>>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 Pro:

Reasoning:  A regular polygon has sides of equal length. Since there are 11 sides and the perimeter is 418m, we can find the length of each side by dividing the total perimeter by the number of sides: 418m / 11 sides = 38m/side. 
### Answer: 38m/side

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 Pro:

Reasoning: The total length of the five sides of the polygon is 56 + 73 + 39 + 24 + 26 = 218m. 
The length of the sixth side is 278 - 218 = 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 Pro:

Reasoning: A pentagon has 5 sides, so we divide the total perimeter by 5 to find the length of one side: 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 Pro:

Reasoning: The ten known sides of the polygon add up to 97m + 93m + 35m + 1m + 27m + 86m + 68m + 96m + 45m + 61m = 609m
The eleventh side must make up the difference between the total perimeter and the sum of the other ten sides, so it is 663m - 609m = 54m long.
### Answer: 54m 

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?

Gemini-1.5 Pro:

Reasoning: The sum of the lengths of the nine known sides of the decagon is 54m + 49m + 85m + 48m + 85m + 19m + 94m + 44m + 54m = 532m
The length of the tenth side is the difference between the total perimeter and the sum of the lengths of the nine known sides, which is 575m - 532m = 43m
### Answer: 43m

Expected answer: 43

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: An octagon has 8 sides of equal length.
The length of each side is 248/8 = <<248/8=31>>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 Pro:

Reasoning: A pentagon has 5 sides. The length of each side of a regular pentagon is equal to its perimeter divided by 5. So, the length of each side of the pentagon is 390/5 = <<390/5=78>>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.

Gemini-1.5 Pro:

Reasoning: The total length of the nine sides is 6m + 85m + 83m + 73m + 25m + 66m + 54m + 87m + 21m = 490m.
The length of the tenth side is 522m - 490m = 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 Pro:

Reasoning: An octagon has 8 sides. The length of each side is equal to the perimeter divided by the number of sides. Therefore the length of each side is 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 Pro:

Reasoning: An octagon has 8 sides.  The length of each side is 696/8 = <<696/8=87>>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 Pro:

Reasoning: An octagon has 8 sides.  To find the length of each side, divide the total perimeter by the number of sides: 744m / 8 = <<744/8=93>>93m.
### 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 Pro:

Reasoning: A nonagon has 9 sides, so to find the length of one side, we divide the perimeter by 9: 270m / 9 = <<270/9=30>>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?

Gemini-1.5 Pro:

Reasoning: The total length of the eight known sides is 30 + 18 + 68 + 23 + 72 + 57 + 33 + 19 = 320 cm
The length of the ninth side is 350 - 320 = 30 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?

Gemini-1.5 Pro:

Reasoning: The total length of the known eight sides of the nonagon is 19m + 7m + 10m + 16m + 32m + 15m + 70m = 169m
The length of the ninth side is 188m - 169m = 19m
### Answer: 19m

Expected answer: 19

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: A hexagon has 6 sides. To find the length of each side, we can divide the total perimeter by the number of sides.
Each side of the hexagon is 90/6 = <<90/6=15>>15 meters long.
### 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?

Gemini-1.5 Pro:

Reasoning: A heptagon has 7 sides, so we divide the total perimeter by the number of sides to find the length of each side: 287m / 7 = <<287/7=41>>41m.
### Answer: 41m 

Expected answer: 41

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: A pentagon has 5 sides. The length of each side is 50/5 = <<50/5=10>>10m. 
### 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 Pro:

Reasoning: A nonagon has 9 sides. 
The length of each side is 63/9 = <<63/9=7>>7 m. 
### 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 Pro:

Reasoning: A hexagon has 6 sides. The length of one side of this hexagon is 354/6 = <<354/6=59>>59 m.
### Answer: 59 m 

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 Pro:

Reasoning: The lengths of the known sides add up to 59m + 16m + 15m + 35m + 89m + 16m + 43m + 7m = 280m.
The length of the last 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?

Gemini-1.5 Pro:

Reasoning: A heptagon has 7 sides, so we divide the total perimeter by the number of sides to find the length of each side: 616m / 7 = <<616/7=88>>88m.
### Answer: 88m 

Expected answer: 88

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: A hexagon has 6 sides. 
Therefore, each side has a length of 36/6 = <<36/6=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 Pro:

Reasoning: The total length of the 11 sides is 88+24+83+64+16+14+90+36+47+88+47 = 597 cm. 
The length of the twelfth side is 987-597 = 390cm.
### Answer: 390cm 

Expected answer: 30

Correct? No

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

Gemini-1.5 Pro:

Reasoning: A hexagon has 6 sides. The length of each side is 306/6 = <<306/6=51>>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 Pro:

Reasoning: A heptagon has 7 sides, so we divide the total perimeter by the number of sides to find the length of each side: 238 meters / 7 sides = <<238/7=34>>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 Pro:

Reasoning: A hexagon has 6 sides. Since it is a regular hexagon, all the sides have the same length.
Therefore, each side has a length of 42/6 = <<42/6=7>>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 Pro:

Reasoning: An octagon has 8 sides.
The length of each side of the octagon is 624/8 = <<624/8=78>>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 Pro:

Reasoning: The first nine sides of the polygon sum up to 17m + 13m + 61m + 16m + 11m + 83m + 28m + 48m + 93m = <<17+13+61+16+11+83+28+48+93=470>>470m. 
The tenth side has a length of 468m - 470m = <<-4>>-4m.
A polygon cannot have a negative side length. It must be the case that the provided side lengths do not correspond to a real polygon.
### Answer: Impossible. 

Expected answer: 98

Correct? No

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

Gemini-1.5 Pro:

Reasoning: A pentagon has 5 sides. 
The length of each side is 380/5 = <<380/5=76>>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 Pro:

Reasoning: An octagon has 8 sides. Since it is a regular octagon, all sides have the same length.  Therefore, the length of one side is 104 cm / 8 = <<104/8=13>>13 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?

Gemini-1.5 Pro:

Reasoning: A heptagon has 7 sides, so we divide the total perimeter by the number of sides to find the length of each side: 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 Pro:

Reasoning: A regular pentagon has 5 equal sides.
The length of each side is 35/5 = <<35/5=7>>7 m.
### Answer: 7 m 

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 Pro:

Reasoning: The total length of the four sides is 45cm + 93cm + 36cm + 22cm = <<45+93+36+22=196>>196cm.
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 Pro:

Reasoning: The lengths of the six sides of the polygon add up to 75+81+22+94+91+10 = <<75+81+22+94+91+10=373>>373cm.
Thus, the length of the last side is 423-373 = <<423-373=50>>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 Pro:

Reasoning: A decagon has 10 sides, so we divide the perimeter by the number of sides to find the length of each side: 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 Pro:

Reasoning: A regular octagon has 8 equal sides. Therefore, the length of each side is 632/8 = <<632/8=79>>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?

Gemini-1.5 Pro:

Reasoning: A septagon has 7 sides, so we divide the total perimeter by 7 to find the length of each side: 161m / 7 = <<161/7=23>>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 Pro:

Reasoning: A hexagon has 6 sides. 
Since it's a regular hexagon, each side has the same length.
Therefore, each side is 96/6 = <<96/6 = 16>>16 meters long.
### 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.

Gemini-1.5 Pro:

Reasoning: The total length of the given eight sides of the nonagon 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 Pro:

Reasoning: A heptagon has 7 sides, so we divide the total perimeter by the number of sides to find the length of each side: 385m / 7 = <<385/7=55>>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 Pro:

Reasoning: The total length of the six given sides of the polygon is 89+2+10+48+94+59 = 302 meters.
Therefore, 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 Pro:

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

Reasoning: An octagon has 8 sides. 
The length of each side is 800/8 = <<800/8 = 100>>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 Pro:

Reasoning: A nonagon has 9 sides.  Since the nonagon is regular, all sides have the same length.  
To find the length of one side, divide the perimeter by the number of sides: 702 m / 9 = <<702/9=78>>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 Pro:

Reasoning: A nonagon has 9 sides. The length of one side is 855/9 = <<855/9=95>>95cm.
### Answer: 95cm

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 Pro:

Reasoning: A heptagon has 7 sides.  The length of a side of a regular polygon is found by dividing the perimeter by the number of sides.
Therefore, the length of a side of the heptagon is 504 meters / 7 = <<504/7=72>>72 meters.
### 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 Pro:

Reasoning: A nonagon has 9 sides.  The length of each side is equal to the perimeter divided by the number of sides, 657/9 = <<657/9=73>>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?

Gemini-1.5 Pro:

Reasoning: A regular octagon has 8 equal sides. To find the length of each side, divide the total perimeter by the number of sides: 48 cm / 8 sides = <<48/8=6>>6 cm/side.
### 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 Pro:

Reasoning: The total length of the known sides is 28m + 37m + 51m + 84m + 54m + 31m + 94m + 12m = 391m.
Therefore, the length of the remaining unknown side is 399m - 391m = 8m.
### 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 Pro:

Reasoning: A nonagon has 9 sides. The length of one side is 342/9 = <<342/9=38>>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 Pro:

Reasoning: The total length of the 7 sides is 7+59+49+38+53+21+34 = <<7+59+49+38+53+21+34=261>>261 m.
The length of the eighth side is 330-261 = <<330-261=69>>69 m.
### 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 Pro:

Reasoning:  Let's call the length of the tenth side "x". The perimeter of a decagon is the sum of all its sides, so we can set up an equation: 88m + 96m + 74m + 52m + 45m + 74m + 85m + 85m + 43m + x = 682m. Combining the known side lengths gives us: 642m + x = 682m. To find x, we can subtract 642m from both sides: x = 682m - 642m = 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 Pro:

Reasoning: A septagon has 7 sides. To find the length of each side, divide the total perimeter by the number of sides.
Each side of the septagon is 161/7 = <<161/7=23>>23m long.
### 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 Pro:

Reasoning: A hexagon has 6 sides. Since it is a regular hexagon, all sides are equal. Therefore, the length of each side is 324/6= <<324/6=54>>54 m.
### Answer: 54 m

Expected answer: 54

Correct? Yes

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

Gemini-1.5 Pro:

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 Pro:

Reasoning: A septagon has 7 sides, and the perimeter is the total length of all the sides added together.  Therefore, the length of each side is the perimeter divided by the number of sides, which is 245m / 7 = <<245/7=35>>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 Pro:

Reasoning: A regular pentagon has 5 sides of equal length.
The length of one side is 25/5 = <<25/5=5>>5cm
### Answer: 5cm 

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 Pro:

Reasoning: The sum of the five sides of the hexagon is 9m + 49m + 100m + 73m + 84m = 315m
The length of the sixth side is 380m - 315m = 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 Pro:

Reasoning: The total length of the known sides is 23+67+57+94+93+18+30 = <<23+67+57+94+93+18+30=382>>382m.
The length of the missing side is 419-382 = <<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 Pro:

Reasoning: A heptagon has 7 sides, so we divide the total perimeter by the number of sides to find the length of each one: 287m / 7 = <<287/7=41>>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 Pro:

Reasoning: A regular pentagon has 5 equal sides. 
The length of each side is 55/5 = <<55/5=11>>11 m.
### Answer: 11 m 

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 Pro:

Reasoning:  A nonagon has 9 sides, and the perimeter is the total length of all the sides added together.  Therefore, we can find the length of one side by dividing the total perimeter by the number of sides: 657 meters / 9 sides = 73 meters/side. 
### 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 Pro:

Reasoning: A hexagon has 6 sides. The length of each side is 78/6 = <<78/6=13>>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 Pro:

Reasoning: An octagon has 8 sides. Since it is a regular octagon, all sides are equal.
Therefore, the length of one side is 600/8 = <<600/8=75>>75 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?

Gemini-1.5 Pro:

Reasoning: The total length of the given sides is 39+26+47+52+66+17+34 = <<39+26+47+52+66+17+34=281>>281 m. 
The length of the last side is 356-281 = <<356-281=75>>75 m.
### Answer: 75 m

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 Pro:

Reasoning: A regular decagon has 10 sides of equal length.
The length of each side equals 930/10 = <<930/10=93>>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 Pro:

Reasoning: First, we find the total length of the known sides: 24m + 25m + 75m + 38m + 18m + 42m + 61m = 283m
Then, we subtract the total length of the known sides from the total perimeter to find the total length of the two unknown sides: 359m - 283m = 76m.
A decagon has 10 sides, and since eight sides are known, the remaining two sides are assumed to be equal. 
Therefore, the length of one side is: 76m / 2 = 38m.
### Answer: 38m

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 Pro:

Reasoning: The total length of the given eight sides of the nonagon is 52m + 52m + 44m + 53m + 41m + 91m + 25m + 2m = 360m. 
The length of the final side 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 Pro:

Reasoning: An octagon has 8 sides. The length of one side is 592/8 = <<592/8=74>>74cm.
### Answer: 74cm

Expected answer: 74

Correct? Yes

Problem: A regular heptagon has a perimeter of 245m. What is the length of each side?

Gemini-1.5 Pro:

Reasoning: A heptagon has 7 sides. The length of each side is 245/7 = <<245/7=35>>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 Pro:

Reasoning: A decagon has 10 sides.
To find the length of each side, we divide the perimeter by the number of sides: 140 m / 10 = 14 m. 
### Answer: 14 m 

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 Pro:

Reasoning: Sum of the lengths of the given 10 sides of the polygon =  44cm + 5cm + 96cm + 78cm + 49cm + 84cm + 72cm + 74cm + 21cm + 39cm = 612 cm
The length of the 11th side = 655cm - 612cm = 43cm.
### Answer: 43cm

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?

Gemini-1.5 Pro:

Reasoning: The total length of the known sides of the polygon is 69m + 81m + 34m + 35m + 38m = <<69+81+34+35+38=257>>257m
The length of the remaining side is 265m - 257m = <<265-257=8>>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 Pro:

Reasoning:
Total length of the four sides = 22 + 14 + 93 + 75 = 204m
The length of the fifth side = 234 - 204 = 30m
### Answer: 30m

Expected answer: 30

Correct? Yes