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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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Bendy Quad

Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

Arclets

Age 14 to 16 Challenge Level:

Each of the following arclets is made from arcs of a circle of radius r.

          

What is the perimeter of an arclet with 3, 4, 5, and n "nodes"?

What happens when n is very large?

Explain the relationship between your answers and the perimeter of the original circle.