the area of the regular pentagon is 6.9 cm². what is the perimeter? 2 cm 5 cm 10 cm 20 cm 1.38 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: Rearrange formula for perimeter

We can rewrite the formula as $p = \frac{2A}{a}$. Given $A = 6.9\ cm^{2}$ and $a=1.38\ cm$.

Step3: Substitute values

$p=\frac{2\times6.9}{1.38}$. $2\times6.9 = 13.8$, so $p=\frac{13.8}{1.38}=10\ cm$.

Answer:

10 cm