Posted by Anonymous on Tuesday, February 5, 2013 at 7:07am.
Let the corners of the square be at (0,0),(1,0),(0,1),(1,1)
y=1-2x intersects y=(1-x)/2 at (1/3,1/3)
So, in each of 4 quadrants, the exterior of the octagon is a trapezoid and a triangle
trapezoid has area 3/16
triangle has area 1/48
sum has area 5/24
The 4 have area 5/6
The octagon thus has area 1/6
Or, consider that the octagon has
side = √5/12
apothem = 1/2√5
area = 1/2 * 8√5/12 * 1/2√5 = 1/6