# Lopsided trapezium

Geometry Level pending

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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