In a parallelogram $ABCD$,the base $AB$ and the corresponding altitude $DM$ are $16 \, cm$ and $12 \, cm$,then the area of $ABCD =$ ................ $cm^{2}$.

Write True or False and justify your answer:
$PQRS$ is a parallelogram whose area is $180 \, cm^{2}$ and $A$ is any point on the diagonal $QS$. The area of $\triangle ASR = 90 \, cm^{2}$.

Two parallelograms are on equal bases and between the same parallels. The ratio of their areas is

In the given figure,$ABED$ is a parallelogram and $DE = EC$. Prove that $\operatorname{ar}(ABF) = \operatorname{ar}(BEC)$.

In $\triangle ABC$,$D$ is the mid-point of $AB$ and $P$ is any point on $BC$. If $CQ \parallel PD$ meets $AB$ in $Q$,then prove that $\operatorname{ar}(\triangle BPQ) = \frac{1}{2} \operatorname{ar}(\triangle ABC)$.

Which of the following figures lie on the same base and between the same parallels? Write the common base and the two parallels for the figure for which the answer is affirmative.