SOLUTION: An artist has been commissioned to make a stained glass window in the shape of a regular octagon. The octagon must fit inside a 26in square space. Determine the length of each side

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Question 1123406: An artist has been commissioned to make a stained glass window in the shape of a regular octagon. The octagon must fit inside a 26in square space. Determine the length of each side of the octagon. Round to the nearest hundredth of an inch.
Answer by greenestamps(13203) About Me  (Show Source):
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Picture the octagon as the 26-inch square with the corners cut off at 45-degree angles. The cut-off corners are 45-45-90 right triangles; the hypotenuse of each of those triangles is a side of the octagon.

Then the 26-inch distance across the square consists of one side of the octagon, plus the legs of two of the triangles.

In a 45-45-90 right triangle, each leg is (1/sqrt(2)) times the length of the hypotenuse. So if x is the length of a side of the octagon, the 26-inch side of the octagon is

%28%281%2Fsqrt%282%29%29%2Ax%29+%2B+%28x%29+%2B+%28%281%2Fsqrt%282%29%29%2Ax%29
or
x%281%2Bsqrt%282%29%29

Then the side length of the octagon is

26%2F%28%281%2Bsqrt%282%29%29%29

which to the nearest hundredth of an inch is 10.77 inches.