Question

question 7 of 10
what is the formula for finding the area of a regular polygon with perimeter p and apothem length a?
a. a = 2pa
b. a = 1/2(pa)
c. a = 1/2(pa)
d. a = 2pa

Explanation:

Step1: Recall area formula

The area $A$ of a regular polygon can be thought of as composed of multiple congruent isosceles - triangles. The sum of the areas of these triangles gives the area of the polygon. The perimeter $P$ is the sum of the lengths of all sides, and the apothem $a$ is the height of each of these isosceles - triangles. The formula for the area of a regular polygon is $A = \frac{1}{2}Pa$, where $P$ is the perimeter and $a$ is the apothem length.

Answer:

B. $A=\frac{1}{2}(Pa)$