Quadrilaterals

  • 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?

  • Square It
    problem

    Square it

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

    Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

  • Parallelogram It
    problem

    Parallelogram it

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

    Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a parallelogram.

  • Rhombus It
    problem

    Rhombus it

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

    Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a rhombus.

  • circles in quadrilaterals
    problem

    Circles in quadrilaterals

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

    Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.

  • Long Short
    problem

    Long short

    Age
    14 to 16
    Challenge level
    filled star filled star empty star
    What can you say about the lengths of the sides of a quadrilateral whose vertices are on a unit circle?
  • A pointed metal arrowhead on the end of an arrow.
    problem

    Arrowhead

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

    The points P, Q, R and S are the midpoints of the edges of a non-convex quadrilateral.What do you notice about the quadrilateral PQRS and its area?

  • Areas of parallelograms
    problem

    Areas of parallelograms

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

    Can you find the area of a parallelogram defined by two vectors?

  • Trapezium Four
    problem

    Trapezium four

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

    The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

  • Bendy Quad
    problem

    Bendy quad

    Age
    14 to 16
    Challenge level
    filled star filled star filled star

    Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.