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Overlapping Beer Mats

Age 11 to 14 Short
Challenge Level

The top beer mat, outlined in red in the diagram below, can be split into triangles from its centre, as shown below.



Because the hexagon is regular, the triangles are all the same, so each one will have area 6 cm$^2$ (since the area of the whole beer mat is 36$=$6$\times$6 cm$^2$).

So, since the overlap consists of 2 of the triangles, its area is 12 cm$^2$.
You can find more short problems, arranged by curriculum topic, in our short problems collection.