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Building Tetrahedra

Can you make a tetrahedron whose faces all have the same perimeter?

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Ladder and Cube

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?

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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.

The London Eye

Stage: 4 Short Challenge Level: Challenge Level:1

Each spoke of the London eye is about $\frac{1}{20}$ mile long. As 1 mile is approximately 1600m this means that the radius of the giant wheel is roughly 80m. So the circumference is approximately 500m.

This problem is taken from the UKMT Mathematical Challenges.