If parallelogram $ABCD$ and rectangle $ABEM$ are of equal area, then:

$ABCD$ is a trapezium with parallel sides $AB=a cm$ and $\mathrm{DC}=b \mathrm{cm}$. $E$and $F$ are the midpoints of the non-parallel sides. The ratio of ar $\left(ABFE\right)$ and ar $\left(EFCD\right)$is

$\mathrm{ABCD}$ is a parallelogram and $\mathrm{X}$ is the midpoint of $\mathrm{AB}$.  If $ar\left(\mathrm{AXCD}\right)=24 {\mathrm{cm}}^2$, then $\mathrm{ar}\left(\mathrm{\Delta ABC}\right)=24{\mathrm{cm}}^2$.

$PQRS$ is a parallelogram whose area is $180 {\mathrm{cm}}^2$and $A$ is any point on the diagonal $QS$. Then, area of $\Delta ASR=90 {\mathrm{cm}}^2$.