### Hallway Borders

What are the possible dimensions of a rectangular hallway if the number of tiles around the perimeter is exactly half the total number of tiles?

### Square Pegs

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

### Boxed In

A box has faces with areas 3, 12 and 25 square centimetres. What is the volume of the box?

# Overlapping Beer Mats

##### Age 11 to 14 ShortChallenge Level

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

You can find more short problems, arranged by curriculum topic, in our short problems collection.