posted by TUHITUHI .
A square whose side is 2m has it's corner cut away so as to form a octagon with all sides equal find the length of each side of octagon and also find the area of the octagon?
if the cutout of each side is x, the side of the octagon is x√2.
Also, 2x + x√2 = 2, so
x = 2-√2
the octagon side s = 2(√2-1)
check: 2(2-√2) + 2(√2-1) = 2
area of octagon with side s = 2s^2 (1+√2)
so, for us, that is 2(1+√2)(2√2-2)^2 = 8(√2-1)