Pebbles

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?

Great Squares

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

Square Areas

Can you work out the area of the inner square and give an explanation of how you did it?

Weekly Problem 42 - 2006

Stage: 3 Challenge Level:

$AB$ is a diameter of a circle of radius 1 cm. Two circular arcs of equal radius are drawn with centres $A$ and $B$. These arcs meet on the circle, as shown. What is the shaded area?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.

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