Area - triangles, quadrilaterals, compound shapes

  • Bicentric Quadrilaterals
    problem

    Bicentric quadrilaterals

    Age
    14 to 16
    Challenge level
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    Investigate the properties of quadrilaterals which can be drawn with a circle just touching each side and another circle just touching each vertex.
  • Maths filler 2
    problem

    Maths filler 2

    Age
    14 to 16
    Challenge level
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    Can you draw the height-time chart as this complicated vessel fills with water?
  • Gutter
    problem

    Gutter

    Age
    14 to 16
    Challenge level
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    Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?

  • Twice as Big?
    problem

    Twice as big?

    Age
    7 to 11
    Challenge level
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    Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

  • Trapezium Four
    problem

    Trapezium four

    Age
    14 to 16
    Challenge level
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    The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

  • Areas of parallelograms
    problem

    Areas of parallelograms

    Age
    14 to 16
    Challenge level
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    Can you find the area of a parallelogram defined by two vectors?

  • Isosceles Triangles
    problem

    Isosceles triangles

    Age
    11 to 14
    Challenge level
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    Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

  • Uncanny triangles
    problem

    Uncanny triangles

    Age
    7 to 11
    Challenge level
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    Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?
  • Tilted Squares
    problem

    Tilted squares

    Age
    11 to 14
    Challenge level
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    It's easy to work out the areas of most squares that we meet, but what if they were tilted?

  • Shear Magic
    problem

    Shear magic

    Age
    11 to 14
    Challenge level
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    Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?