Calculate the area of the quadrangular shaded region ($S_3$), if $[S_1] = 18\ \mathrm{m}^2$, $[S_2] = 4.5\ \mathrm{m}^2$, and $MNCL$ is a parallelogram.
(Answer: $27\ \mathrm{m}^2$)
(Drawing not to scale)
Some relations I found: If $BL$ passes through $T$ (meeting of the trapezoidal diagonals) then $AL = LC$ \begin{align*} S_{ABL}&=S_{BLC},\\ S_{BMN}&=\frac{S_{ABC}}{4},\\ S_{AML}&=S_{MBN}. \end{align*}