How long are the sides of an equiangular octagon if the height is 6 inches?

Question

For the height, I mean the distance from one side to the other. I need to make some patterns but I don't know how long the sides need to be.

Answer 1

If you draw a diagram (or look at this one: http://www.pagetutor.com/octagon_layout/octagon.gif ), you should see that the height of the octagon is one full side length and 2 45-degree side lengths.

h = s + 2s/√2 = s + s√2 = s(1 + √2)

So:

6 = s(1 + √2)

s = 6/(1 + √2) ≈ 2.485 inches, or just a smidge less than 2 1/2".