Question

find the area of a regular polygon with 7 sides, an apothem of 8 meters, and a side length of 7.7 meters. round to the nearest tenth.

Explanation:

Step1: Calculate the perimeter

The perimeter \(P\) of a regular polygon is \(P = n\times s\), where \(n\) is the number of sides and \(s\) is the side - length.
Given \(n = 7\) and \(s=7.7\) meters, then \(P=7\times7.7 = 53.9\) meters.

Step2: Use the area formula for a regular polygon

The area formula for a regular polygon is \(A=\frac{1}{2}\times a\times P\), where \(a\) is the apothem and \(P\) is the perimeter.
Given \(a = 8\) meters and \(P = 53.9\) meters.
Substitute the values into the formula: \(A=\frac{1}{2}\times8\times53.9\).
First, calculate \(\frac{1}{2}\times8=4\).
Then, \(A = 4\times53.9=215.6\) square meters.

Answer:

\(215.6\)