If I have an octagon that is 12 feet across (side to opposite side) how can I find the length of the sides?
I assume you have a regular octagon so you can think of it as a 12 ft by 12 ft square with the corners cut off. Suppose that each side has length S.
In the diagram the corner triangle, ABC, has |CA| = |BC| and thus using the theorem of Pythagoras
2 |CA|2 = S2
|CA| = S/
Since the octagon is 12 feet across,
S = 4.97 feet