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

Answer 1

Hello!

The answer is: $332in^{2}$

Why?

From the statement we know that the octagon has a apothem of 10in and a perimeter of 66.3in, and we are asked to find the area of the octagon.

We can use the following formula:

$A=\frac{Perimeter*Apothem}{2}$

Substituting the given information into the area formula, we have:

$A=\frac{66.3in*10in}{2}\\\\A=\frac{663in}{2}=331.5in^{2}$

Rounding to the nearest number we have that:

331.5 ≈ 332

So, the area of the octagon is: $332in^{2}$

Have a nice day!

Answer 2

Answer:

$332in^2$

Step-by-step explanation:

The area of a regular polygon is calculated using the formula;

$Area=\frac{1}{2}ap$

where $a$ is the apothem and p is the perimeter.

It was given that, the apothem is, $a=10in.$ and the perimeter is $p=66.3 in.$

We substitute into the formula to obtain;

$Area=\frac{1}{2}\times10\times66.3in^2$

$Area=331.5in^2$

To the nearest square inch, we have;

$Area=332in^2$