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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