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

$A$ villager,Itwaari,has a plot of land in the shape of a quadrilateral. The Gram Panchayat of the village decided to take over some portion of his plot from one of the corners to construct a Health Centre. Itwaari agrees to the above proposal with the condition that he should be given an equal amount of land in lieu of his land,adjoining his plot,so as to form a triangular plot. Explain how this proposal will be implemented.

Diagonals $AC$ and $BD$ of a trapezium $ABCD$ with $AB || DC$ intersect each other at $O$. Prove that $ar(AOD) = ar(BOC).$

In the figure,$E$ is any point on the median $AD$ of a $\Delta ABC$. Show that $\text{ar} (ABE) = \text{ar} (ACE)$.

Show that a median of a triangle divides it into two triangles of equal areas.