Question

find the area of the regular polygon. round to the nearest hundredths.
15 in
17.32 in

Explanation:

Step1: Recall the formula for the area of a regular polygon

The formula for the area of a regular polygon is \(A=\frac{1}{2}aP\), where \(a\) is the apothem and \(P\) is the perimeter.

Step2: Calculate the perimeter \(P\)

A regular hexagon has \(n = 6\) sides. Given the side length \(s=17.32\) in. The perimeter \(P=ns\), so \(P = 6\times17.32=103.92\) in.

Step3: Identify the apothem \(a\)

The apothem \(a = 15\) in.

Step4: Substitute into the area formula

Substitute \(a = 15\) and \(P=103.92\) into \(A=\frac{1}{2}aP\). Then \(A=\frac{1}{2}\times15\times103.92\).
First, calculate \(\frac{1}{2}\times15 = 7.5\). Then \(A=7.5\times103.92\).
\(A = 779.4\) in².

Answer:

\(779.40\) in²