Problem 1
Answer: Approximately 172.04774 square inches
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Work Shown:
In this case, we have n = 5 sides and each side is x = 10 units long
A = area of regular polygon
A = 0.25*n*x^2*cot(180/n)
A = 0.25*5*10^2*cot(180/5)
A = 172.04774
cot stands for cotangent, and cot(x) = 1/( tan(x) ). Your calculator needs to be in degree mode for the formula above to work. This formula only applies to regular polygons.
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Problem 2
Answer: Approximately 309.019336 square cm.
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Work Shown:
We'll use the same formula as problem 1. This time we know that there are n = 8 sides. The perimeter is 64, so each side is x = 64/n = 64/8 = 8.
So,
A = 0.25*n*x^2*cot(180/n)
A = 0.25*8*8^2*cot(180/8)
A = 309.019336