What is the actual square footage of a 12' octagon?


I am going to assume that you have a regular octagon and that the width is 12 feet (w in the diagram below). I am going to think of this octagon as a square with the four corners cut off as in the diagram.

The four pieces cut off can be arranged into two squares with sides of length b feet and hence the area of the octagon is w 2 - 2 b 2 square feet. Since w = 12 feet, all that is needed is to find b.

From the diagram

w = b + S + b = S + 2b. Also each of the cut off pieces is a right triangle and hence, by Pythagoras' Theorem, S 2 = b 2 + b 2 = 2 b 2 Thus or

Hence the area is

square feet which is approximately 119 square feet.

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