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 formula for the area of a regular polygon is $A=\frac{1}{2}ap$, where $a$ is the apothem and $p$ is the perimeter.

Step2: Identify apothem and side - length

The apothem $a = 24.9$ inches and the side - length of the regular polygon is $s=24$ inches.

Step3: Calculate the perimeter

For a regular polygon, if the number of sides is $n$ and the side - length is $s$, the perimeter $p=ns$. Assuming this is an octagon ($n = 8$), $p=8\times24=192$ inches.

Step4: Calculate the area

Substitute $a = 24.9$ and $p = 192$ into the area formula $A=\frac{1}{2}ap$. So $A=\frac{1}{2}\times24.9\times192$. First, $\frac{1}{2}\times192 = 96$, then $A=24.9\times96=2390.4$.

Answer:

$2390.4$