Assuming that the octagon is regular, what is the area of the shaded region below? Use your calculator and round your final answer to the nearest hundredth.

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anonymous · Answer

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anonymous · Answer

You would find the area of both the octagon and the square, and then subtract the area of the square from the area of the octagon. Do you know how to find the area of the figures? If not I can help.

anonymous · Answer

Okay, well, I'm going to help you anyway :P

First off, a right octagon means all sides are the same length as well as all the angles the same measure. So everything is equal in that closed shape. So you know that all the sides are the same length. Also, it gives you the Apothem length: which is the length from the middle of the polygon to the midpoint of one of the sides. $$Area= \frac{ 1 }{ 2 } (Perimeter) (Apothem) $$Since you know the Apothem, all you need to know is the perimeter. That can be easily found because all the sides are the same length, and it tells you that one of the sides = 13. Plug in the equation to get:$$Area = \frac{ 1 }{ 2 }(104)(15.69)$$ Solve and that is the area of your octagon. You should get 815.88. Now you find the area of the square. Which I hope you know how to do. Length times Width. That should get you 169. Now all that's left is to take the area of the octagon (815.88) and subtract the area of the square (169). What does that give you? 646.88 units = the shaded part. And there you go!