Question

find the area of the regular polygon. round to the nearest hundredths.
17 ft
4.9 ft

Explanation:

Step1: Find the perimeter

A regular triangle (equilateral triangle) has 3 equal sides. Each side \(s = 17\) ft.
Perimeter \(P=3s\)
\(P = 3\times17=51\) ft

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 (\(a = 4.9\) ft) and \(P\) is the perimeter.
Substitute \(a = 4.9\) and \(P = 51\) into the formula:
\(A=\frac{1}{2}\times4.9\times51\)
First, calculate \(4.9\times51 = 249.9\)
Then, \(A=\frac{1}{2}\times249.9=124.95\)

Answer:

\(124.95\) square feet