\(ABCD\) 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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