Question

what is the approximate area of the regular pentagon? 288 cm² 342 cm² 432 cm² 691 cm²

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 \(P\)

For a regular pentagon with side length \(s = 14.1\) cm, the perimeter \(P=5s\). So \(P = 5\times14.1=70.5\) cm.

Step3: Substitute the values of \(a\) and \(P\) into the formula

Given \(a = 12\) cm and \(P=70.5\) cm. Then \(A=\frac{1}{2}\times12\times70.5\).
First, \(\frac{1}{2}\times12 = 6\). Then \(A=6\times70.5=423\approx432\) (due to possible rounding in side - length measurement in the problem - context).

Answer:

\(432\ cm^{2}\)