# Polka Dots in Pi

Geometry Level 4

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

$$EAH, FBE,GCF,HDG$$ are quadrants. There are two semicicles with diameters $$AD$$ and $$BC$$.

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

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

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

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