Polka Dots in Pi

Geometry Level 4

In the figure, ABCDABCD is a square of side length aa units and E,F,G,HE,F,G,H are the midpoints of the sides.

EAH,FBE,GCF,HDGEAH, FBE,GCF,HDG are quadrants. There are two semicicles with diameters ADAD and BCBC.

If the area of the shaded region in red can be expressed in the form

a2x(yπz) \dfrac{a^2}x \left( \sqrt y - \dfrac\pi z\right)

then submit xyz \dfrac {xy} z as your answer.

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