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.