### 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?

# Triangle in the Corner

##### Age 11 to 14 ShortChallenge Level

The diagram shows a regular hexagon with an area of $48$ m$^2$.

What is the area of the shaded triangle?

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.