A trapezium is divided into four triangles by its diagonals. Suppose the two triangles containing the parallel sides have areas a and b, what is the area of the trapezium?

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. . . .

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

Three rods of different lengths form three sides of an enclosure with right angles between them. What arrangement maximises the area

A small circle in a square in a big circle in a trapezium. Using the measurements and clue given, find the area of the trapezium.

Rotate a copy of the trapezium about the centre of the longest side of the blue triangle to make a square. Find the area of the square and then derive a formula for the area of the trapezium.