Regular polygons and circles

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Hex

Age

11 to 14

Challenge level

Explain how the thirteen pieces making up the regular hexagon shown in the diagram can be re-assembled to form three smaller regular hexagons congruent to each other.
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Quadarc

Age

14 to 16

Challenge level

Given a square ABCD of sides 10 cm, and using the corners as centres, construct four quadrants with radius 10 cm each inside the square. The four arcs intersect at P, Q, R and S. Find the area enclosed by PQRS.
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Approximating Pi

Age

14 to 18

Challenge level

By inscribing a circle in a square and then a square in a circle find an approximation to pi. By using a hexagon, can you improve on the approximation?
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What Shape and Colour?

Age

5 to 7

Challenge level

Can you fill in the empty boxes in the grid with the right shape and colour?
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2 Rings

Age

5 to 7

Challenge level

The red ring is inside the blue ring in this picture. Can you rearrange the rings in different ways? Perhaps you can overlap them or put one outside another?
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Olympic Rings

Age

5 to 7

Challenge level

Can you design your own version of the Olympic rings, using interlocking squares instead of circles?
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Shaping It

Age

5 to 11

Challenge level

These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.
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Always, Sometimes or Never? Shape

Age

7 to 11

Challenge level

Are these statements always true, sometimes true or never true?
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Bracelets

Age

7 to 11

Challenge level

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
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Sweets in a Box

Age

7 to 11

Challenge level

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?