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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.

If ABCD is a square of area 1. E, F are mid points of AB and BC respectively. What is the area of blue region?

The given figure shows a circle, centred at O, enclosed in a square. Find the total area of shaded parts?

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In the figure, if ABCD and EFGC are squares with areas R and S respectively. What is the area of the blue region?

In a unit square, two quarter circles are drawn, centered at two opposite vertices, What is the area of the oval-shaped region?