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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?

Weekly Problem 44 - 2006

Stage: 3 Challenge Level: Challenge Level:1


The area of the rectangle is $6 \times 8 = 48$ square units, so the unshaded area is $\frac{1}{4} \times 48 = 12$ square units. Therefore $(\frac{1}{2} \times x \times 2) + (\frac{1}{2} \times (6-x) \times 8) = 12$, that is, $x + 24 - 4 x = 12$, so $x=4$.

This problem is taken from the UKMT Mathematical Challenges.

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