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 area - perimeter formula

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

Step2: Identify given values

We are given that $A = 6.9\ cm^{2}$ and $a=1.38\ cm$.

Step3: Solve for perimeter

Substitute the given values into the formula $A=\frac{1}{2}ap$. We get $6.9=\frac{1}{2}\times1.38\times p$. First, simplify the right - hand side: $\frac{1}{2}\times1.38 = 0.69$. So the equation becomes $6.9 = 0.69p$. Then, solve for $p$ by dividing both sides of the equation by $0.69$: $p=\frac{6.9}{0.69}=10\ cm$.

Answer:

C. 10 cm