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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?

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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?

Inscribed in a Circle

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

The area of a square inscribed in a circle with a unit radius is, satisfyingly, $2$.

What is the area of a regular hexagon inscribed in a circle with a unit radius?

Circle within a hexagon

What is the area of an equilateral triangle inscribed in a circle with a unit radius?

Triangle within a circle