Question

a regular octagon has an apothem measuring 10 in. and a perimeter of 66.3 in. what is the area of the octagon, rounded to the nearest square inch? 88 in.² 175 in.² 332 in.² 700 in.²

Explanation:

Step1: Recall the formula for the area of a regular polygon

The formula for the area \(A\) of a regular polygon is \(A=\frac{1}{2}aP\), where \(a\) is the apothem and \(P\) is the perimeter.

Step2: Substitute the given values into the formula

Given \(a = 10\) in and \(P=66.3\) in. Then \(A=\frac{1}{2}\times10\times66.3\).

Step3: Calculate the value

First, \(\frac{1}{2}\times10 = 5\). Then \(A=5\times66.3=331.5\).

Step4: Round the result

Rounding \(331.5\) to the nearest square inch gives \(332\).

Answer:

C. \(332\ \text{in.}^2\)