Area - triangles, quadrilaterals, compound shapes

  • Rati-o
    problem

    Rati-O

    Age
    11 to 14
    Challenge level
    Points P, Q, R and S each divide the sides AB, BC, CD and DA respectively in the ratio of 2 : 1. Join the points. What is the area of the parallelogram PQRS in relation to the original rectangle?
  • 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 Island
    problem

    Triangle Island

    Age
    7 to 11
    Challenge level
    You have pitched your tent (the red triangle) on an island. Can you move it to the position shown by the purple triangle making sure you obey the rules?
  • Uncanny triangles
    problem

    Uncanny Triangles

    Age
    7 to 11
    Challenge level
    Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?
  • Triangle transformation
    problem

    Triangle Transformation

    Age
    7 to 14
    Challenge level
    Start with a triangle. Can you cut it up to make a rectangle?
  • Dotty triangles
    problem

    Dotty Triangles

    Age
    11 to 14
    Challenge level

    Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?

  • Isosceles
    problem

    Isosceles

    Age
    11 to 14
    Challenge level

    Prove that a triangle with sides of length 5, 5 and 6 has the same area as a triangle with sides of length 5, 5 and 8. Find other pairs of non-congruent isosceles triangles which have equal areas.

  • 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?

  • Disappearing square
    problem

    Disappearing Square

    Age
    11 to 14
    Challenge level

    Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. Do you have any interesting findings to report?

  • 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?

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