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UKMT Intermediate Mathematical Challenge, 2018

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

The diagram shows a triangle with edges of length 3, 4 and 6. A circle of radius 1 is drawn at each vertex of the triangle. What is the total shaded area?

(A) $2\pi$ (B) $\frac{9\pi}{4}$ (C) $\frac{5\pi}{2}$ (D) $\frac{11\pi}{4}$ (E) $3\pi$

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