Problem of the Week 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 $$ABCD$$.