Question

find the area of a regular octagon with an apothem of 7 inches and a side length of 5.8 inches. round to the nearest tenth.

Explanation:

Step1: Calculate the perimeter

The formula for the perimeter \(P\) of a regular octagon is \(P = 8s\), where \(s\) is the side - length. Given \(s = 5.8\) inches, then \(P=8\times5.8 = 46.4\) inches.

Step2: Use the area formula for regular polygons

The formula for the area \(A\) of a regular polygon is \(A=\frac{1}{2}aP\), where \(a\) is the apothem and \(P\) is the perimeter. Given \(a = 7\) inches and \(P = 46.4\) inches. Then \(A=\frac{1}{2}\times7\times46.4\).
First, calculate \(7\times46.4 = 324.8\). Then \(A=\frac{324.8}{2}=162.4\) square inches.

Answer:

\(162.4\)