Which of the following figures lie on the same base and between the same parallels? In such a case,write the common base and the two parallels.

In the figure,$ABCD$ is a parallelogram and $EFCD$ is a rectangle. Also,$AL \perp DC$. Prove that:
$(i)$ $\text{ar}(ABCD) = \text{ar}(EFCD)$
$(ii)$ $\text{ar}(ABCD) = DC \times AL$

In the figure,$ABCD$ is a parallelogram,$AE \perp DC$ and $CF \perp AD$. If $AB = 16 \, cm, AE = 8 \, cm$ and $CF = 10 \, cm$,find $AD$. (in $, cm$)

In the figure,$ABC$ is a right triangle right-angled at $A$. $BCED$,$ACFG$,and $ABMN$ are squares on the sides $BC$,$CA$,and $AB$ respectively. Line segment $AX \perp DE$ meets $BC$ at $Y$. Show that: $\operatorname{ar}(CYXE) = 2 \operatorname{ar}(FCB)$.

In the figure,$ABCDE$ is a pentagon. $A$ line through $B$ parallel to $AC$ meets $DC$ produced at $F$. Show that:
$(i)$ $ar(ACB) = ar(ACF)$
$(ii)$ $ar(AEDF) = ar(ABCDE)$

$XY$ is a line parallel to side $BC$ of a triangle $ABC$. If $BE || AC$ and $CF || AB$ meet $XY$ at $E$ and $F$ respectively,show that $\operatorname{ar}(ABE) = \operatorname{ar}(ACF)$.