Question

calculate the area of the regular polygon. enter the answer in the space provided. use numbers instead of words. square inches

Explanation:

Step1: Recall area formula for regular polygon

The area formula for a regular polygon is $A = \frac{1}{2}ap$, where $a$ is the apothem and $p$ is the perimeter. The apothem is the distance from the center of the polygon to the mid - point of a side. Here, the apothem $a = 60$ in and assume the side length is $s = 52$ in.

Step2: Calculate the perimeter

For an octagon (8 - sided polygon), the perimeter $p=8s$. Substituting $s = 52$ in, we get $p = 8\times52=416$ in.

Step3: Calculate the area

Substitute $a = 60$ in and $p = 416$ in into the area formula $A=\frac{1}{2}ap$. So $A=\frac{1}{2}\times60\times416$.
$A = 30\times416=12480$ square inches.

Answer:

12480