### Building Tetrahedra

Can you make a tetrahedron whose faces all have the same perimeter?

### Ladder and Cube

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

### Areas and Ratios

What is the area of the quadrilateral APOQ? Working on the building blocks will give you some insights that may help you to work it out.

# Pencil Turning

##### Stage: 4 Short Challenge Level:
See all short problems arranged by curriculum topic in the short problems collection

A pencil AB lying on a table is given a half turn about the end B (so that A moves to A*) and then a half turn about A* (so that B moves to B*). The point C on the pencil is one third of the way from A to B.

What is the ratio of the total distances moved by A and by C?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.