Question

the area of the regular pentagon is 6.9 cm². what is the perimeter? 2 cm 5 cm 10 cm 20 cm

Explanation:

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

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

Step2: Substitute the given values into the formula

We are given that \(A = 6.9\space cm^{2}\) and \(a=1.38\space cm\). Substituting into \(A=\frac{1}{2}ap\), we get \(6.9=\frac{1}{2}\times1.38\times p\).

Step3: Solve for \(p\)

First, simplify the right - hand side: \(\frac{1}{2}\times1.38 = 0.69\). Then the equation becomes \(6.9 = 0.69p\). Divide both sides by \(0.69\): \(p=\frac{6.9}{0.69}=10\).

Answer:

\(10\space cm\)