The lateral sides of a trapezium have length equal to \(30\) and \(50.\) A circle can be inscribed in the trapezium, tangent to all its sides. The line connecting the midpoints of the lateral sides divides the area of the trapezium in the ratio \(5:11.\) Find the product of the lengths of the bases of the trapezium.

**Details and assumptions**

A trapezium has a pair of parallel sides.

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