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 28in square space. Determine the length of each side

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Question 1165390: An artist has been commissioned to make a stained glass window in the shape of a regular octagon. The octagon must fit inside a 28in square space. Determine the length of each side of the octagon. Round to the nearest hundredth of an inch.
Answer by greenestamps(13216) About Me  (Show Source):
You can put this solution on YOUR website!


Picture the regular octagon as the 28-inch square, with isosceles right triangles cut off each corner.

If s is the length of each side of the octagon, then each leg of each of the isosceles triangles is s%2Fsqrt%282%29.

Then the 28-inch side of the square is composed of the legs of two of the isosceles triangles and one side of the octagon. Its length is s%2B2%28s%2Fsqrt%282%29%29+=+s%2Bs%2Asqrt%282%29+=+s%281%2Bsqrt%282%29%29

So

s%281%2Bsqrt%282%29%29+=+28
s+=+28%2F%281%2Bsqrt%282%29%29

Use a calculator and round as directed.