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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?


What is the minimum number of squares a 13 by 13 square can be dissected into?

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.

Coloured Edges

Age 11 to 14 Challenge Level:

Why do this problem?

This problem requires learners to work logically with numbers and shapes at the same time. The best ways of finding a solution include using a letter to represent the length of the side of the square.

Key questions

What sort of number of tiles must you use to make a square?
What sort of number of tile edges will make up the perimeter of the square?
Have you thought of using a letter to represent the length of the side of the square?

Possible extension

Learners could try to arrange the tiles so that touching edges are all the same colour. They could also try Painting Cubes which is a similar problem.

Possible support

Suggest making a list of possible square numbers. Then using squared paper and colouring the edges of the small squares within a suitably sized larger square and finding the answer by trial and improve.