### Right Time

At the time of writing the hour and minute hands of my clock are at right angles. How long will it be before they are at right angles again?

### Isosceles

Prove that a triangle with sides of length 5, 5 and 6 has the same area as a triangle with sides of length 5, 5 and 8. Find other pairs of non-congruent isosceles triangles which have equal areas.

Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?

# 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.