Question

calculate the area of the regular polygon. 60 in. 52 in. > 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 $a = 52$ in. The side length of the octagon is $s=60$ in.

Step2: Calculate the perimeter

For an octagon ($n = 8$), the perimeter $P=ns$. So $P = 8\times60=480$ in.

Step3: Calculate the area

Substitute $a = 52$ in and $P = 480$ in into the area formula $A=\frac{1}{2}aP$. Then $A=\frac{1}{2}\times52\times480$. First, $\frac{1}{2}\times52 = 26$, and then $26\times480=12480$ square inches.

Answer:

12480