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, which is $a = 60$ in.

Step2: Calculate the perimeter

For a regular octagon with side length $s=52$ in, the perimeter $P$ of an octagon is $P = 8s$. So $P=8\times52=416$ in.

Step3: Calculate the area

Substitute $a = 60$ in and $P = 416$ in into the area formula $A=\frac{1}{2}aP$. We get $A=\frac{1}{2}\times60\times416$. First, $\frac{1}{2}\times60 = 30$, then $30\times416=12480$ square inches.

Answer:

12480