Overlapping beer mats

Can you find the area of the overlap when these two beer mats are placed on top of each other?
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Two beer mats, each the shape of a regular hexagon with area 36cm$^2$, are placed on top of each other, as shown below.

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Overlapping beer mats
 

If they are placed so that the corner of the lower beer mat is in the centre of the higher beer mat, as shown below, what is the area of the overlap?

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Overlapping beer mats


If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is adapted from the World Mathematics Championships