Question

question 2 of 10
what is the formula for finding the area of a regular polygon with perimeter p and apothem length a?
a. a = ½(pa)
b. a = ½(pa)
c. a = pa
d. a = pa

Explanation:

Step1: Recall area - polygon relationship

A regular polygon can be divided into congruent isosceles triangles. The area of each triangle is $\frac{1}{2}\times base\times height$. The sum of the bases of these triangles is the perimeter $P$ of the polygon, and the height of each triangle is the apothem $a$.

Step2: Derive the formula

The area $A$ of the regular polygon is the sum of the areas of these isosceles triangles. Since the area of each triangle is $\frac{1}{2}\times base\times height$ and the sum of bases is $P$ and height is $a$, we get $A=\frac{1}{2}(Pa)$.

Answer:

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