Quadrilaterals

  • Small pepper seedlings in turquoise pots.
    problem

    Square Bisection

    Age
    11 to 14
    Challenge level

    Weekly Problem 8 - 2008
    In how many ways can a square be cut in half using a single straight line cut?

  • Small pepper seedlings in turquoise pots.
    problem

    Outside the Nonagon

    Age
    11 to 14
    Challenge level

    Weekly Problem 44 - 2010
    Extend two of the sides of a nonagon to form an angle. How large is this acute angle?

  • Making Rectangles, Making Squares
    problem

    Making Rectangles, Making Squares

    Age
    11 to 14
    Challenge level
    How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?
  • Linkage
    problem

    Linkage

    Age
    11 to 14
    Challenge level

    Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?

  • Small pepper seedlings in turquoise pots.
    problem

    Dividing the Field

    Age
    14 to 16
    Challenge level

    A farmer has a field which is the shape of a trapezium as illustrated below. To increase his profits he wishes to grow two different crops. To do this he would like to divide the field into two trapeziums each of equal area. How could he do this?

  • Long Short
    problem

    Long Short

    Age
    14 to 16
    Challenge level

    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

    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?

  • Small pepper seedlings in turquoise pots.
    problem

    Unusual Quadrilateral

    Age
    14 to 16
    Challenge level

    This quadrilateral has an unusual shape. Are you able to find its area?

  • Cyclic Quad Jigsaw
    problem

    Cyclic Quad Jigsaw

    Age
    14 to 16
    Challenge level

    A picture is made by joining five small quadrilaterals together to make a large quadrilateral. Is it possible to draw a similar picture if all the small quadrilaterals are cyclic?

  • Bicentric Quadrilaterals
    problem

    Bicentric Quadrilaterals

    Age
    14 to 16
    Challenge level
    Investigate the properties of quadrilaterals which can be drawn with a circle just touching each side and another circle just touching each vertex.
Displaying 51 - 60 of 65