# Picking Equal Areas

Geometry Level pending

$$ABCD$$ is a right trapezium with $$\angle DAB = \angle ABC = 90^\circ$$, $$AB = 12$$, $$BC = 32$$ and $$AD = 16$$. $$E$$ is a point on $$DC$$ such that $$[ABED] = [BEC]$$. What is the value of $$BE^2$$?

Details and assumptions

$$[PQRS]$$ denotes the area of $$PQRS$$.

A trapezium has a pair of parallel sides.

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