Question

calculate the area of the regular polygon.
8 cm
16 cm

enter the answer in the space provided. use numbers instead of words.

square centimeters

Explanation:

Step1: Recall area formula for regular polygon

The formula for the area of a regular polygon is $A=\frac{1}{2}ap$, where $a$ is the apothem (the distance from the center of the polygon to the mid - point of a side) and $p$ is the perimeter. Here, the apothem $a = 8$ cm and the side length $s=16$ cm.

Step2: Calculate the perimeter

For a regular pentagon (5 - sided polygon), the perimeter $p=ns$, where $n = 5$ and $s = 16$ cm. So $p=5\times16=80$ cm.

Step3: Calculate the area

Substitute $a = 8$ cm and $p = 80$ cm into the area formula $A=\frac{1}{2}ap$. We get $A=\frac{1}{2}\times8\times80$.
$A = 320$ square centimeters.

Answer:

320