Following figures shows a unit square ABCD. If the area of the octagon (in blue) can be expressed as 1/a find a?
In similar triangles W.BC and HXC WB is half of BC therefore HX is half of WB i.e. 0.5*0.5=0.25 units. Thus HV=0.25 also. The vertex angle of HVI is 350/8 = 45. Solution of the isosceles triangle HVI gives its height as 0.23097 and half of base as 0.095671. Thus area of one triangle is 0.23097*0.095671=0.022097. Thus area of the regular octagon =8* 0.022097=0.176777 units. The inverse of this is 5.656854. This corroborates solution over internet.
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