What a clever little piece of mathematics this is. It is a much neater proof of Pythagoras Theorem than the one I was shown at school. There were also some very well laid out solutions with clear explanations, so well done.

Complete solutions were received from:

Aftab Hussain - whose solution is given below,
Michael Brooker (home educated),
Andrei Lazanu (School number 205, Bucharest),
Charles Blackham (Shrewsbury House School).

Here is Aftab's solution:

Area of the square = (a+b) ² (square of sides a+b)

Area of the Trapezium = Area of square divided by 2 (rotational symmetry)

Area of Trapezium as a sum of areas of triangles

Proof

Area of Trapezium derived from square = Area of Trapezium as a sum of areas of three triangles.