2D shapes and their properties

  • 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?
  • Always, Sometimes or Never? KS1
    problem
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    Always, Sometimes or Never? KS1

    Age
    5 to 7
    Challenge level

    Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

  • Shapely Lines
    problem
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    Shapely Lines

    Age
    5 to 7
    Challenge level

    This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?

  • What's happening?
    problem
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    What's Happening?

    Age
    5 to 7
    Challenge level

    Shapes are added to other shapes. Can you see what is happening? What is the rule?

  • Triangle or No Triangle?
    problem
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    Triangle or No Triangle?

    Age
    5 to 7
    Challenge level

    Here is a selection of different shapes. Can you work out which ones are triangles, and why?

  • Chain of Changes
    problem
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    Chain of Changes

    Age
    5 to 7
    Challenge level

    In this activity, shapes can be arranged by changing either the colour or the shape each time. Can you find a way to do it?

  • 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?

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