Area Inside an Obtuse Triangle
Triangle \(ABC\) has an obtuse angle at \(B\), base \(BC\) has length equal to \(30\) and height equal to \(24\). (This height is taken with respect to base \(BC\)). \(D\) is a point on the line segment \(BC\) and \(E\) is a point on \(AC\) such that \(DE \parallel AB\). \(F\) is a point on \( AB\) such that \(FD \parallel AC\). As \(D\) varies within line segment \(BC\), what is the maximum value of \( [DEF] \)?
Details and assumptions
\([PQRS]\) denotes the area of the figure \(PQRS\).