Regular polygons and circles

  • Where are they?
    problem
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    Where Are They?

    Age
    7 to 11
    Challenge level
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    Use the isometric grid paper to find the different polygons.

  • problem
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    Round and Round the Circle

    Age
    7 to 11
    Challenge level
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    What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

  • Egyptian Rope
    problem
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    Egyptian Rope

    Age
    7 to 11
    Challenge level
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    The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

  • Shapes on the Playground
    problem
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    Shapes on the Playground

    Age
    7 to 11
    Challenge level
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    Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?

  • Overlapping Again
    problem
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    Overlapping Again

    Age
    7 to 11
    Challenge level
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    What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

  • Tessellation interactivity
    interactivity
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    Tessellation Interactivity

    Age
    7 to 16
    Challenge level
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    An environment that enables you to investigate tessellations of regular polygons
  • Rolling Around
    problem
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    Rolling Around

    Age
    11 to 14
    Challenge level
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    A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

  • problem
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    Salinon

    Age
    14 to 16
    Challenge level
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    This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?

  • Curvy areas
    problem
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    Curvy Areas

    Age
    14 to 16
    Challenge level
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    Have a go at creating these images based on circles. What do you notice about the areas of the different sections?

  • Semi-detached
    problem
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    Semi-Detached

    Age
    14 to 16
    Challenge level
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    A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.