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.

Trisected Triangle

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

The diagram below shows four types of tile, each of which is made up of one or more equilateral triangles.

For how many of these types of tile can we place three identical copies of the tile together, without gaps or overlaps, to make an equilateral triangle?

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

This problem is taken from the UKMT Mathematical Challenges.