Two beer mats, each the shape of a regular hexagon with area 36cm$^2$, are placed on top of each other, as shown below.

 

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?






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