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Trapezium and Diagonals

The opposite corners of a trapezium are joined, creating four triangles within the trapezium. The areas of the triangles formed using the parallel sides as is given. The task is to calculate the areas of the other two triangles.

Working out the general result involves using ideas of similarity, area scale factor, length scale factor, multiplying out brackets and working with square roots. The final answer is a very elegant relationship between the triangle areas.

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