Answer
(24 + 12$\sqrt 3$) $in^{2}$
Work Step by Step
Given that in a regular polygon of 12 sides, the measure of each side is 2in and the measure of apothem is (2 +$\sqrt 3$ ) in
We need to find out the area of this regular polygon
The perimeter of the given polygon is P = 12 * s = 12 * 2
=24 in
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 = $\frac{1}{2}$ (2 +$\sqrt 3$ ) * 24
= (24 + 12$\sqrt 3$) $in^{2}$
