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### Number and algebra

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### Working mathematically

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### For younger learners

# Tilted Squares

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Age 11 to 14

Challenge Level

- Problem
- Getting Started
- Student Solutions
- Teachers' Resources

Two standard methods for working out the areas of shapes may help.

Boxing in the tilted squares, working out the area of the box and subtracting the areas of the unwanted right-angled triangles:

Splitting the tilted squares into right-angled triangles and squares and adding the areas of the different parts:

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?