Question

find the area of the regular polygon.
6.2 mm
9 mm

Explanation:

Step1: Find the perimeter

A regular pentagon has 5 sides. Given side length \(s = 9\) mm.
Perimeter \(P=5\times s = 5\times9=45\) mm.

Step2: Use the area formula for regular polygons

The area formula for a regular polygon is \(A=\frac{1}{2}aP\), where \(a = 6.2\) mm (apothem) and \(P = 45\) mm (perimeter).
\(A=\frac{1}{2}\times6.2\times45\)
First, calculate \(\frac{1}{2}\times6.2 = 3.1\).
Then, \(A=3.1\times45=139.5\) \(mm^{2}\).

Answer:

\(139.5\) \(mm^{2}\)