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 in² 175 in² 332 in² 700 in²

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.

Step2: Substitute given values

Given $a = 10$ in and $p=66.3$ in. Substitute into the formula: $A=\frac{1}{2}\times10\times66.3$.

Step3: Calculate the area

$A = 5\times66.3=331.5$ in².

Step4: Round to nearest square - inch

Rounding $331.5$ to the nearest square - inch gives $332$ in².

Answer:

$332$ in²