Regular polygons and circles

  • Hex
    problem
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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.
  • Quadarc
    problem
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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.
  • Approximating Pi
    problem
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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?
  • 2 Rings
    problem
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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?

  • Olympic rings
    problem
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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?

  • Shaping It
    problem
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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.
  • A section of a bracelet made of colourful beads.
    problem
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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?

  • problem
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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?

  • Where are they?
    problem
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    Where Are They?

    Age
    7 to 11
    Challenge level

    Use the isometric grid paper to find the different polygons.

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