In regular octagon ABCDEFGH, M and N are midpoints of line BC and line FG respectively. Compute [ABMO]/[ABCDEFGH]. ([ABCD] denotes the area of polygon ABCD.)
If we break everything into little triangles, (ABO, BOC, etc) we'll notice that ABMO = 1.5 triangles, and there are 8 triangles in total.
1.5/8 = 3/16