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

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. . . .

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?

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.

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