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?

Dividing a Square

Age 11 to 14 ShortChallenge Level
Three lines have been drawn from the centre of this square to split it into two congruent trapezia and a pentagon.

The side length of the square is 1, and the areas of the three shapes are all equal.

What is the length $x$?

This problem is adapted from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.