Area - triangles, quadrilaterals, compound shapes

problem

Square Pizza

Age

14 to 16

Challenge level

Can you show that you can share a square pizza equally between two people by cutting it four times using vertical, horizontal and diagonal cuts through any point inside the square?
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?
problem

Rod Area

Age

7 to 11

This task challenges you to create symmetrical U shapes out of rods and find their areas.
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?
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?
problem

Triangle Transformation

Age

7 to 14

Challenge level

Start with a triangle. Can you cut it up to make a rectangle?
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.
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?
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?
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?