Building Tetrahedra

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

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.

Centre Square

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

The diagram shows two identical large circles and two identical smaller circles whose centres are at the corners of a square. The two large circles are touching, and they each touch the two smaller circles. The radius of the small circles is $1cm$. What is the radius of the large circles in centimetres?

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.