SOLUTION: A regular polygon has a 170 diagonals and 2.4 cm side length. What is its area?

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Question 810700: A regular polygon has a 170 diagonals and 2.4 cm side length. What is its area?
Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
The number of sides and number of diagonals in a polygon is related by: %28n%5E2+-+3n%29%2F2+=+d where n is the number of sides and d is the number of diagonals.


n%5E2+-+3n+=+340


n%5E2+-+3n+-+340+=+0


(n+17)(n-20) = 0 so n=-17 or 20. A polygon can't have a negative number of sides, so n = 20.


One formula for the area of a regular polygon given the number of sides and length of sides is Area = %28n%2AS%5E2%29%2F4tan%28pi%2Fn%29 where n is the number of sides, S is the length of a side, and TAN is taken in radians.


Area of this polygon = 20%2A%282.4%5E2%29%2F4tan%28pi%2F20%29 = approximately 181.8 cubic centimeters.