Area - triangles, quadrilaterals, compound shapes

  • Triangle in a Trapezium
    problem

    Triangle in a trapezium

    Age
    11 to 16
    Challenge level
    filled star filled star empty star

    Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?

  • The Farmers' Field Boundary
    problem

    The farmers' field boundary

    Age
    11 to 14
    Challenge level
    filled star filled star empty star

    The farmers want to redraw their field boundary but keep the area the same. Can you advise them?

  • Rod Area
    problem

    Rod area

    Age
    7 to 11

    This task challenges you to create symmetrical U shapes out of rods and find their areas.

  • Triangle transformation
    problem

    Triangle transformation

    Age
    7 to 14
    Challenge level
    filled star empty star empty star
    Start with a triangle. Can you cut it up to make a rectangle?
  • Completing Quadrilaterals
    problem

    Completing quadrilaterals

    Age
    11 to 14
    Challenge level
    filled star empty star empty star

    We started drawing some quadrilaterals - can you complete them?

  • Towering Trapeziums
    problem

    Towering trapeziums

    Age
    14 to 16
    Challenge level
    filled star filled star empty star
    Can you find the areas of the trapezia in this sequence?
  • Quadrilaterals in a Square
    problem

    Quadrilaterals in a square

    Age
    11 to 14
    Challenge level
    filled star filled star empty star

    What's special about the area of quadrilaterals drawn in a square?

  • Triangles in a Square
    problem

    Triangles in a square

    Age
    11 to 14
    Challenge level
    filled star empty star empty star

    What are the possible areas of triangles drawn in a square?

  • Kite in a Square
    problem

    Kite in a square

    Age
    14 to 18
    Challenge level
    filled star filled star empty star

    Can you make sense of the three methods to work out what fraction of the total area is shaded?

  • Growing Rectangles
    problem

    Growing rectangles

    Age
    11 to 14
    Challenge level
    filled star empty star empty star

    What happens to the area and volume of 2D and 3D shapes when you enlarge them?