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UKMT Intermediate Mathematical Challenge, 2023

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

A semicircle of radius 3 units is drawn on one edge of a right-angled triangle, and a semicircle of radius 4 units is drawn on another edge. The semicircles intersect on the hypotenuse of the triangle, as shown. What is the shaded area, in square units?

(A) $\dfrac{25\pi}{2} - 24$ (B) $12$ (C) $\dfrac{25\pi}{2} - 6$ (D) $25\pi - 24$ (E) $24$

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