Sweet Red Fish

Geometry Level 3

The figure above shows that a large circle with radius 5 cm5\text{ cm} is inscribed in a square and another circle with diameter 5 cm5\text{ cm} is only half inside that square.

Calculate the area of the shaded region (colored red) in the figure. Give your answer in cm2 \text{cm}^2 to three decimal places.

Details and Assumptions:

  • You may use the approximation π=3.14159 \pi = 3.14159 and sin1(45)=0.92729 \sin^{-1} \left ( \frac 4 5 \right ) = 0.92729 .

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