Quadrilaterals

  • Trapezium Four
    problem
    Favourite

    Trapezium Four

    Age
    14 to 16
    Challenge level

    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
    Favourite

    Bendy Quad

    Age
    14 to 16
    Challenge level

    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.

  • Trapezium made of wooden tangram pieces, including a square and a parallelogram.
    problem
    Favourite

    Quad in Quad

    Age
    14 to 18
    Challenge level

    Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?

  • Flexi Quads
    problem
    Favourite

    Flexi Quads

    Age
    16 to 18
    Challenge level

    A quadrilateral changes shape with the edge lengths constant. Show the scalar product of the diagonals is constant. If the diagonals are perpendicular in one position are they always perpendicular?

  • Lawnmower
    problem

    Lawnmower

    Age
    14 to 16
    Challenge level
    A kite shaped lawn consists of an equilateral triangle ABC of side 130 feet and an isosceles triangle BCD in which BD and CD are of length 169 feet. A gardener has a motor mower which cuts strips of grass exactly one foot wide and wishes to cut the entire lawn in parallel strips. What is the minimum number of strips the gardener must mow?
  • Placeholder: several colourful numbers
    problem

    Quadrilaterals in a Hexagon

    Age
    7 to 14
    Challenge level
    Which of these quadrilaterals can you find in the hexagon?
  • Biggest Bendy
    problem

    Biggest Bendy

    Age
    16 to 18
    Challenge level
    Four rods are hinged at their ends to form a quadrilateral. How can you maximise its area?
  • Strange Rectangle
    problem

    Strange Rectangle

    Age
    16 to 18
    Challenge level
    ABCD is a rectangle and P, Q, R and S are moveable points on the edges dividing the edges in certain ratios. Strangely PQRS is always a cyclic quadrilateral and you can find the angles.
  • Cutting it Out
    problem

    Cutting It Out

    Age
    5 to 11
    Challenge level
    I cut this square into two different shapes. What can you say about the relationship between them?
  • Folding Flowers 1
    problem

    Folding Flowers 1

    Age
    7 to 11
    Challenge level

    Can you visualise what shape this piece of paper will make when it is folded?

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