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Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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Great Squares

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

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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?

Tangram Area

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2
tangram with lengths marked
The parallelogram has base $6 \; \text{cm}$ and height $3 \; \text{cm}$, so area $6 \; \text{cm} \times 3 \; \text{cm} = 18\; \text{cm}^{2} $

Alternatively, notice that if you rearrange the parallelogram into a rectangle, you can tile the square with eight of them. Therefore the area of the parallelogram is $144 \div 8 = 18 \text{cm}^{2}$

This problem is taken from the UKMT Mathematical Challenges.