Regular Polygon- Geometry

Let the number of sides be 2n. Let the length of the side be S and the length of the perpendicular from the centre to each side be P. Since the number of sides is even , the opposite sides will be parallel and the distance between any two opposite sides is equal to 2P.

Also , area of the polygon (A) = 2n ( SP/2) —- (1)

Given that S (2P) = A/4 or SP = A/8

Therefore A = n ( A/8)

n = 8 or 2n = 16