Question

find the area of a regular pentagon with an apothem of 6 inches and a side length of 8.7 inches.
round to the nearest tenth.

Explanation:

Step1: Calculate the perimeter

A regular pentagon has 5 sides. Given side length \(s = 8.7\) inches.
Perimeter \(P=5s\)
\(P = 5\times8.7=43.5\) inches.

Step2: Use the area formula for regular polygons

The area formula for a regular polygon is \(A=\frac{1}{2}aP\), where \(a\) is the apothem and \(P\) is the perimeter. Given \(a = 6\) inches and \(P=43.5\) inches.
\(A=\frac{1}{2}\times6\times43.5\)
First, \(\frac{1}{2}\times6 = 3\)
Then \(A=3\times43.5=130.5\) square inches.

Answer:

\(130.5\)