Question

What is the area of a regular polygon with perimeter
58 and apothem 10 ?

Answer 1

Let the length of each side be 2a.
Then perimeter
= 2an where n is the number of sides in the polygon.
So 2an = 58 and an = 29.
The number of triangles which make up the area of polygon = n and the area of
Of each triangle = apothem * a = 10a.

So, area of polygon = 10an = 10*29
= 290.