### 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:

Have you tried some simple cases to see if there is a pattern?

If you have a number "$x$" the next number is "$x +1$". How could you write four consecutive numbers?

If you can express $x^4 + \ldots + 16$ as a perfect square, the two factors will be of the form $(x^2 +\ldots + 4)$.