Aregular 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?
10 in
88 in 2
175 in 2
332 in2
700 in 2

Option C. 332 in²

Step-by-step explanation:

In the figure attached, a regular octagon has been drawn with all equal sides and apothem OP = 10 in.

Perimeter of the given octagon is given as 66.3 in

We have to calculate the area of the octagon.

As we can see in the figure an octagon is a combination of 8 triangles.

So we will find the area of one triangle first.

Area of ΔBOC =

Since perimeter of octagon = 8 × one side = 8×BC

66.3 = 8× BC

BC =

BC = 8.288 in

Therefore, area of ΔBOC =

= 5×8.288

= 41.44 in²

Now area of octagon ABCDEFGH = 8×41.44 = 331.5 ≈ 332 in²

Therefore, area of the regular octagon will be 332 in²

Option C. is the answer.

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