### 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.

# Always Perfect

##### Stage: 4 Challenge Level:

$2 \times3 \times4 \times5 + 1 = 11^2$
$21 \times22 \times23 \times24 + 1 = 505^2$

Show that if you add $1$ to the product of four consecutive numbers the answer is ALWAYS a perfect square.