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.)
Draw BO and CO
[ABO ] = (1/8) of the octagon's area
[BCO ] = (1/8) of the octagon's area
And
[BMO ] = (1/2) [ BCO ] = 1/16 of the octagon's area
And [ ABO ] + [ BMO ] = [ ABMO ] = (1/8) + (1/16) = (3/16) of the octagon's area
So
[ABMO ] / [ ABCDEFGH] = 3 / 16
