In the diagram above, $\square BCDE$ is a rectangle with horizontal side length $30$ cm and vertical side length $6$ cm. Line segments $\overline{BD}$ and $\overline{CE}$ are diagonals of $\square BCDE,$ which intersect at point $O$. Point $M$ is the bisector of $\overline{BE},$ and the extension of lines $\overline{DM}$ and $\overline{CB}$ intersect at point $A.$ If point $F$ is the intersection of $\overline{CE}$ and $\overline{AD},$ what is the area of $\triangle DOF?$

Note: The above figure is not drawn to scale.