Question

Explain how the formula for the area of a regular polygon is derived from that of a triangle.

Answer 1

take for example a square which is a regular polygon
if we divide the square in two congruent triangles then

A of square = 1/2( b x h ) + 1/2 (b x h)
A = 1/2 (s x s) + 1/2 (s x s)
= 1/2 S^2 + 1/2 S^2
= S^2