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2001 Spatial Oddity

With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.

Screwed-up

A cylindrical helix is just a spiral on a cylinder, like an ordinary spring or the thread on a bolt. If I turn a left-handed helix over (top to bottom) does it become a right handed helix?

Counting Triangles

Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether?

Making Rectangles, Making Squares

Age 11 to 14 Challenge Level:

Imagine you have any number of equilateral triangles all of the same size as well as a large number of $30$ $^\circ$ , $30$ $^\circ$ , $120$ $^\circ$ isosceles triangles with the shorter sides the same length as the equilateral triangles.

Using these triangles how many differently shaped rectangles can you build?

Can you make a square?

 
Printable NRICH Roadshow resource.