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=(Perimeter*Apothem)/(2)`

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

`A=(66.3in*10in)/(2)\\\\A=(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

`332in^2`

Explanation:

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

`Area=(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=(1)/(2)*10*66.3in^2`

`Area=331.5in^2`

To the nearest square inch, we have;

`Area=332in^2`