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

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kudzordzifrancis kudzordzifrancis · Answer 1 · 2019-04-17T19:13:35+02:00

Answer:

[tex]332in^2[/tex]

Step-by-step explanation:

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

[tex]Area=\frac{1}{2}ap[/tex]

where [tex]a[/tex] is the apothem and p is the perimeter.

It was given that, the apothem is, [tex]a=10in.[/tex] and the perimeter is [tex]p=66.3 in.[/tex]

We substitute into the formula to obtain;

[tex]Area=\frac{1}{2}\times10\times66.3in^2[/tex]

[tex]Area=331.5in^2[/tex]

To the nearest square inch, we have;

[tex]Area=332in^2[/tex]

mixter17 mixter17 · Answer 2 · 2019-04-17T19:23:27+02:00

The answer is: [tex]332in^{2}[/tex]

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:

[tex]A=\frac{Perimeter*Apothem}{2}[/tex]

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

[tex]A=\frac{66.3in*10in}{2}\\\\A=\frac{663in}{2}=331.5in^{2}[/tex]

Rounding to the nearest number we have that:

331.5 ≈ 332

So, the area of the octagon is: [tex]332in^{2}[/tex]

Have a nice day!