### 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.

# Ratio Riddle

##### Stage: 4 Short Challenge Level:
$9 : 8$
$$\frac{b}{c} = \frac{a}{c} \times\frac{b}{a}= \frac{3}{4} \times\frac{3}{2} = \frac{9}{8}$$

This problem is taken from the UKMT Mathematical Challenges.