ABCD is square and PQRSTUVW is octagon with equal sides constructed with in the square.
In order to have octagon with equal sides, we should have AP=QB=BR=SC=CT=….
Let AP=AW=x;
Let PQ = y; as all sides of octagon are equal, QR=RS=ST=TU=UV=VW=WP=y;
As the length of side of square is 2,
2x+y = 2 ------(1)
Applying Pythagoras to the right triangle APW, y2 = x2+x2 = 2x2
=> y= x√2 ------(2)
Solving (1) and (2):
2x+x√2 = 2 => x = 2/(2+√2) = √2/(√2+1)
=> y = x√2 = 2/(√2+1)
