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UKMT Intermediate Mathematical Challenge, 2016

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

The tiling pattern shown uses two types of tile, regular hexagons and equilateral triangles, with the length of each side of the equilateral triangles equal to half the length of each side of the hexagons. A large number of tiles is used to cover a floor. Which of the following is closest to the fraction of the floor that is shaded black?

(A) $\frac{1}{8}$ (B) $\frac{1}{10}$ (C) $\frac{1}{12}$ (D) $\frac{1}{13}$ (E) $\frac{1}{16}$

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