SOLUTION: The area of a regular polygon is 36 square inches. Find the length of a side if the polygon has the given number of sides. Round your answer to the nearest tenth. a. 3 b. 4

Algebra ->  Surface-area -> SOLUTION: The area of a regular polygon is 36 square inches. Find the length of a side if the polygon has the given number of sides. Round your answer to the nearest tenth. a. 3 b. 4       Log On


   

Question 581438: The area of a regular polygon is 36 square inches. Find the length of a side if the polygon has the given number of sides. Round your answer to the nearest tenth.
a. 3 b. 4 c. 6
d. Suppose the polygon is a pentagon. What would you expect the lenght of its side to be? Explain.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The area of a regular polygon is 36 square inches. Find the length of a side if the polygon has the given number of sides. Round your answer to the nearest tenth.
a. 3 b. 4 c. 6
-----------
Area+=+ns%5E2%2Acot%28180%2Fn%29%2F4 where n = # of sides & s = side length
s%5E2+=+4%2AArea%2Atan%28180%2Fn%29%2Fn
s+=+sqrt%284%2AArea%2Atan%28180%2Fn%29%2Fn%29+=+sqrt%28144%2Atan%28180%2Fn%29%2Fn%29
n = 3: --> s = 9.118 inches
n = 4: --> s = 6.000 inches
n = 5: --> s = 4.574 inches
n = 6: --> s = 3.722 inches
d. Suppose the polygon is a pentagon. What would you expect the lenght of its side to be?
It's between the lengths of 4 & 6. As the # of sides increases, the length decreases.
n = 20 --> s = 1.06788 inches
----------------------