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UKMT Senior Mathematical Challenge, 2022

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

The perimeter of a logo is created from two vertical straight edges, two small semicircles with horizontal diameters and two large semicircles. Both of the straight edges and the diameters of the small semicircles have length $2$ . The logo has rotational symmetry as shown. What is the shaded area?

(A) $4$ (B) $4-\pi$ (C) $8$ (D) $4+\pi$ (E) $12$

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