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UKMT Junior Mathematical Olympiad, 2019

Geometry Difficulty 2.0 Junior Prove it United Kingdom

The diagram alongside shows two quarter-circles and two triangles, $ABC$ and $CDE$ . One quarter-circle has radius $AB$ , where $AB = 3$ cm. The other quarter-circle has radius $DE$ , where $DE = 4$ cm. The area enclosed by the line $AE$ and the arcs of the two quarter-circles is shaded. What is the total shaded area, in $\text{cm}^2$ ?

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