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This activity investigates how you might make squares and pentominoes from Polydron.

Tiles on a Patio

How many ways can you find of tiling the square patio, using square tiles of different sizes?

My New Patio

What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?


Age 7 to 11 Challenge Level:

Geraldine and Suzanne sent in their solutions to this problem. They said:

We think there are five different squares which you can make on a 4 by 4 geoboard. Here is a picture of three of them:

three squares

Here is a picture of the other two which only have pegs at their corners, not along their sides:

tilted squares

The pink square in the second picture has an area of two square units. We don't think you can make a square with an area of three square units as the next size up square we have has sides of 2 which means its area is 4 square units (too big).