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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.

Where to Land

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Chris is swimming in a lake, 50m from the shore.
Her family are 100m along the shore.


She'd like to get back to her family as quickly as possible. If she can swim at 3 m/sec and run at 7m/sec, how far along the shore should she land in order to get back as quickly as possible?