If $ar(PQRS) = 80 \, cm^2$ for a parallelogram $PQRS$,then $ar(PSR) = \dots \dots \dots cm^2$.

In the given figure,$PQM$ is a line and $SQ || RM$. Prove that $ar(PQR) = ar(PMS)$.

The figure obtained by joining the mid-points of the adjacent sides of a rectangle of sides $8 \, cm$ and $6 \, cm$ is:

In $\triangle ABC$,$AD$ is a median. $E$ is the midpoint of $BD$ and $O$ is the midpoint of $AE$. Prove that $ar(AOB) = \frac{1}{8} ar(ABC)$.

$ABCD$ is a rectangle. If $AB = 12 \, cm$ and $BC = 7 \, cm$,then find the area of $ABCD$ in $cm^2$.

In parallelogram $ABCD$,$AB = 12 \, cm$. Altitudes $DM$ and $DN$ correspond to bases $AB$ and $BC$ respectively. If $DM = 5 \, cm$ and $DN = 6 \, cm$,then find the length of $BC$ in $cm$.