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UKMT Senior Kangaroo, 2017

Geometry Difficulty 2.0 Junior Prove it United Kingdom

The pattern shown in the diagram is constructed using semicircles. Each semicircle has a diameter that lies on the horizontal axis shown and has one of the black dots at either end. The distance between each pair of adjacent black dots is 1 cm. The area, in cm $^2$ , of the pattern that is shaded in grey is $\frac{1}{8}k\pi$ . What is the value of $k$ ?

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