Question

find the area of a regular decagon with an apothem of 5 meters and a side length of 3.25 meters.
round to the nearest tenth.

Explanation:

Step1: Calculate the perimeter

A decagon has \(n = 10\) sides. Given side length \(s=3.25\) meters.
Perimeter \(P=ns\)
\(P = 10\times3.25=32.5\) meters

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 \(a = 5\) meters and \(P=32.5\) meters.
\(A=\frac{1}{2}\times5\times32.5\)
\(A=\frac{162.5}{2}=81.25\)

Answer:

\(81.3\)