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Square Areas

Can you work out the area of the inner square and give an explanation of how you did it?

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.

Tetra Square

ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.


Age 11 to 14 Challenge Level:

It is certainly worthwhile looking at gradually increasing the size of the squares. With younger pupils it would be good to allow them to discuss the situation for even sided squares and those with a side that is a multiple of 3. For older/more able pupils its a good idea to go at least as far as a 43 by 43 square! When a large number have been tried I would suggest that pupils try to examine their "system" for getting the least number of squares.