Parallelograms on the Same Base and between Same Parallels

In the figure, if parallelogram $PQFE$ and rectangle $PQRS$ are of equal area, then which of the following is true?

In the given figure, $ABCD$ and $ABPQ$ are two parallelograms and $M$ is a point on $AQ$ and $BMP$ is a triangle. Then, $ar(△BMP)=\frac{1}{2}ar( \square ABCD)$ is 

In the figure, if parallelogram $PQFE$ and rectangle $PQRS$ are of equal area, then which of the following is true?

In the figure below, BD || AC and AD || CE.

Identify the triangles whose areas are equal.

In the given figure, $\mathrm{P}\mathrm{Q}\mathrm{R}\mathrm{S}$ is a parallelogram such that $\mathrm{S}\mathrm{L}\perp \mathrm{P}\mathrm{Q}, \mathrm{Q}\mathrm{N}\perp \mathrm{P}\mathrm{S}$ and $\mathrm{Q}\mathrm{M}\perp \mathrm{S}\mathrm{R}$. Then which of the following gives the area of the parallelogram $\mathrm{P}\mathrm{Q}\mathrm{R}\mathrm{S}$?

Given that the area of parallelogram $\mathrm{ABFE}$ is $25 {\mathrm{cm}}^2$. Also $\mathrm{DE}=\mathrm{AE}$. If the area of the parallelogram $\mathrm{ABCD}$ is $k {\mathrm{cm}}^2$, find the value of $k$.