Question

a regular pentagon has an apothem measuring 3 cm and a perimeter of 21.8 cm. what is the area of the pentagon, rounded to the nearest tenth? 13.8 cm² 17.3 cm² 32.7 cm² 69.0 cm²

Explanation:

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

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

Step2: Substitute the given values into the formula

Given \(a = 3\space\text{cm}\) and \(P=21.8\space\text{cm}\). Then \(A=\frac{1}{2}\times3\times21.8\).
First, calculate \(3\times21.8 = 65.4\). Then \(\frac{1}{2}\times65.4=32.7\).

Answer:

\(32.7\space\text{cm}^2\) (the third option)