Answer
128($\sqrt 2$ -1) $cm^{2}$
Work Step by Step
Given that in a regular polygon of 8 sides, the measure of apothem is 4 cm and the measure of each side is 8($\sqrt 2$ -1) cm
We need to find out the area of this regular polygon
The perimeter of the given polygon is P = 8 * s = 8 * 8($\sqrt 2$ -1)
= 64($\sqrt 2$ -1) cm
The area of a regular polygon whose apothem has length a and whose perimeter P is given by A = $\frac{1}{2}$ ap
The area of the given regular polygon = $\frac{1}{2}$* 4 * 64($\sqrt 2$ -1) cm
= 128($\sqrt 2$ -1) $cm^{2}$
