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July 29, 2016
Posted by **Anonymous** on Tuesday, February 5, 2013 at 7:07am.

- maths-urgently needed -
**Steve**, Tuesday, February 5, 2013 at 11:15amLet 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