Answer:
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 = ![\frac{1}{2}(BC)(OP)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%28BC%29%28OP%29)
Since perimeter of octagon = 8 × one side = 8×BC
66.3 = 8× BC
BC = ![\frac{66.3}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B66.3%7D%7B8%7D)
BC = 8.288 in
Therefore, area of ΔBOC = ![\frac{1}{2}(10)(8.288)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%2810%29%288.288%29)
= 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.