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UKMT Pink Kangaroo, 2015

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

The diagram shows a square with sides of length $a$ . The shaded part of the square is bounded by a semicircle and two quarter-circle arcs. What is the shaded area?

(A) $\frac{\pi a^2}{8}$ (B) $\frac{a^2}{2}$ (C) $\frac{\pi a^2}{2}$ (D) $\frac{a^2}{4}$ (E) $\frac{\pi a^2}{4}$

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