### 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.

# Circled Corners

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

The three angles of the triangle add to $180^{\circ}$, so the combined area of the three sectors of the circles that are inside the triangle add up to half a circle with area:

$\frac{1}{2} \times \pi \times 2^2 = \frac {4\pi}{2}= 2\pi$.

So the grey area is $(80- 2\pi) cm^2$.

This problem is taken from the UKMT Mathematical Challenges.