SOLUTION: An artist has been commissioned to make a stained glass window in the shape of a regular octagon. The octagon must fit inside an 18-in. square space. Determine the length of each s

Question 1009297: An artist has been commissioned to make a stained glass window in the shape of a regular octagon. The octagon must fit inside an 18-in. square space. Determine the length of each side of the octagon. Round to the nearest hundredth of an inch
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Let the side of the octagon be x.
If you draw the diagram of it, you will notice that
x + x/sqrt(2) + x/sqrt(2) = 18
since the sloping sides are hypotenuses of 45-45-90 right triangles.
Factor out x and get
x(1 + 2/sqrt(2)) = 18
x(1 + sqrt(2)) = 18
x = 18/(1+sqrt(2)) = 7.457 in
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