ABCD is a trapezium in which AB is parallel to DC. Let E and F be the midpoints on AD and BC respectively. If EF=10 cm and AB-DC=4 cm, then what is the value of AB \times DC?

Explanation

The segment joining the midpoints of the non-parallel sides is EF = \frac{AB + DC}{2} = 10 \implies AB + DC = 20. We are given AB - DC = 4. Solving these gives 2AB = 24 \implies AB = 12 cm, and DC = 8 cm. Therefore, AB \times DC = 12 \times 8 = 96 square cm.

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