SOLUTION: Find the area of a regular octagon inscribed in a circle with radius r with 45 degree

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Question 1040353: Find the area of a regular octagon inscribed in a circle with radius r with 45 degree
Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
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Find the area of a regular octagon inscribed in a circle with radius r. highlight%28cross%28with_45_degree%29%29.
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This octagon is comprised of 8 isosceles triangles, each with two lateral sides of the length r and the angle of 360%2F8 = 45 degrees between them.

Very good.

Then the area of each of these triangles is half of the product r by itself and sin(45°)  
(see the lesson Formulas for area of a triangle in this site).

In other words, S1 = %281%2F2%29%2Ar%5E2%2Asin45%5Eo%29 = %281%2F2%29%2Ar%5E2%2A%28sqrt%282%29%2F2%29 = %28r%5E2%2Asqrt%282%29%29%2F4.

Now multiply it by 8, and you will get S = 2%2Asqrt%282%29%2Ar%5E2 for the area of the entire octagon.