### 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.

# Isosceles Reduction

##### Stage: 4 Short Challenge Level:
See all short problems arranged by curriculum topic in the short problems collection

$PQR$ is a triangle and $S$ is a point on $QR$.
$QP=QR=9$ cm and $PR = PS =6$ cm.
What is the length of $SR$?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.