### 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.

# Platinum Puzzle

##### Stage: 4 Short Challenge Level:

The volume of $1\textrm{ kg}$ of platinum is $(1000/21.45)\textrm{ cm}^3$, that is approximately $50\textrm{ cm}^3$. So $1$ tonne of platinum has an approximate volume of $50,000\textrm{ cm}^3$, or $1/20\textrm{ m}^3$. So about $5\textrm{ m}^3$ of platinum is produced per year, and so the total volume ever produced is $250\textrm{ m}^3%$. This is the same as a volume of a cuboid measuring $10\textrm{ m}\times5\textrm{ m}\times5\textrm{ m}$, which is similar to the size of a house.

This problem is taken from the UKMT Mathematical Challenges.