# Sweet Red Fish

Geometry Level 4

The figure above shows that a large circle with radius $$5\text{ cm}$$ is inscribed in a square and another circle with diameter $$5\text{ cm}$$ is only half inside that square.

Calculate the area of the shaded region (colored red) in the figure. Give your answer in $$\text{cm}^2$$ to three decimal places.

Details and Assumptions:

• You may use the approximation $$\pi = 3.14159$$ and $$\sin^{-1} \left ( \frac 4 5 \right ) = 0.92729$$.
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