### 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.

# Annulus Area

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

Ans: 28%

The area of the larger circle is 25$\pi$ cm $^2$.
The area of the smallest circle is 9$\pi$ cm $^2$.
The area of the middle circle is 16$\pi$ cm $^2$.
Therefore the area of the ring is (16$\pi$ - 9 $\pi$) cm $^2$ i.e. 7 $\pi$ cm $^2$.

Therefore the percentage shaded is 28%.

This problem is taken from the UKMT Mathematical Challenges.