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UKMT Intermediate Mathematical Challenge, 2017

Geometry Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

The diagram shows seven circular arcs and a heptagon with equal sides but unequal angles. The sides of the heptagon have length $4$ . The centre of each arc is a vertex of the heptagon, and the ends of the arc are the midpoints of the two adjacent sides. What is the total shaded area?

(A) $12\pi$ (B) $14\pi$ (C) $16\pi$ (D) $18\pi$ (E) $20\pi$

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