SOLUTION: I need help with this question. If the apothem is 12cm, and the perimeter is 81.6, then what is the area of a regular n-gon?

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Question 1101217: I need help with this question.
If the apothem is 12cm, and the perimeter is 81.6, then what is the area of a regular n-gon?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
The area of a regular n-gon = half the product of the apothem and the perimeter = 

%281%2F2%29%2A12%2A81.6 = 489.6 cm^2.


Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The area of a triangle is one-half the base times the height.

In a regular polygon with n sides, if you picture it as n congruent isosceles triangles, the apothem is the height of each triangle, and the perimeter of the polygon is the sum of the bases of all the triangles.

So the area of a regular a regular n-gon with apothem 12 and perimeter 81.6 is %281%2F2%29%2881.6%29%2812%29+=+489.6