### 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.

# Platinum Puzzle

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

Platinum is a very rare metal, even rarer than gold. Its density is $21.5\textrm{ g/cm}^3$. Assuming that the world production has been about $110$ tonnes for each of the past $50$ years, and negligible before that, which of the following has a comparable volume to that of the total amount of platinum ever produced?

A: a shoe box, B: a cupboard, C: a house, D: Buckingham Palace, E: the grand Canyon

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.