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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.

Dissect

Age 11 to 14 Challenge Level:

The minimum number of squares a 13 by 13 square can be dissected into is 11:

There is one trivial solution to the size of the smallest square which can be dissected into squares which are all different sizes: the unit square! The smallest non-unit square which can be dissected into squares which are all different sizes has sides of length 175 units.

For further information on this and other similar problems see Chapter 11, Mrs. Perkins Quilt and Other Square-Packing Problems in Mathematical Carnival by Martin Gardner, published by Pelican books.