Quadrilaterals

  • Strange Rectangle 2
    problem

    Strange rectangle 2

    Age
    16 to 18
    Challenge level
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    Find the exact values of some trig. ratios from this rectangle in which a cyclic quadrilateral cuts off four right angled triangles.
  • Strange Rectangle
    problem

    Strange rectangle

    Age
    16 to 18
    Challenge level
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    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.
  • Long Short
    problem

    Long short

    Age
    14 to 16
    Challenge level
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    What can you say about the lengths of the sides of a quadrilateral whose vertices are on a unit circle?
  • Lawnmower
    problem

    Lawnmower

    Age
    14 to 16
    Challenge level
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    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?
  • Biggest Bendy
    problem

    Biggest bendy

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

    Bendy quad

    Age
    14 to 16
    Challenge level
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    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.
  • Set Square
    problem

    Set square

    Age
    16 to 18
    Challenge level
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    A triangle PQR, right angled at P, slides on a horizontal floor with Q and R in contact with perpendicular walls. What is the locus of P?
  • Part the Polygons
    problem

    Part the polygons

    Age
    7 to 11
    Challenge level
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    Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.
  • Is a Square a Rectangle?
    problem

    Is a square a rectangle?

    Age
    7 to 11
    Challenge level
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    How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?
  • Cut and Make
    problem

    Cut and make

    Age
    7 to 11
    Challenge level
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    Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?