Problem D

The Whole Rectangle

In the diagram, \(ABCD\) is a rectangle. Points \(F\) and \(G\) are on \(DC\) (with \(F\) closer to \(D\)) such that \(DF=FG=GC\). Point \(E\) is the midpoint of \(AD\).

If the area of \(\triangle BEF\) is \(30\text{ cm}^2\), determine the area of rectangle \(ABCD\).