A regular octagon is formed by cutting off the corners of a square. If one side of the square is n cm, find the total area removed in square cm.

Answer 1

If the length of the corners cut off is s, the diagonal length is s√2.

The area of each triangle is thus 1/2 (2s^2) = s^2

Now, we know that 2s + s√2 = n, so

s = n/(1+√2)

The area cut off is thus 4n^2/(3+2√2) = 4(3-√8)n^2