A trapezoid¹ is divided into four triangles by its diagonals.  Let the triangles adjacent to the parallel sides have areas A and B.  Find the area of the trapezoid in terms of A and B.

Trapezoid, divided into four triangles by its diagonals

(1) A trapezoid is a quadrilateral with at least one pair of parallel sides.  In some countries, such a quadrilateral is known as a trapezium.

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