A villager Itwaari has a plot of land of 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 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.

Let ABCD be the Itwaari’s plot.
Join BD and Throught C draw a line CF parallel to BD which meet AB Produced at F.
Now join D and F.
Triangles CBD and FBD are on the same base BD and between same parallels BD ∥ CF.
Hence, ar(CBD = ar(FBD)
[∵ Triangles on the same base (or equal bases) and between the same parallels are equal in area.]
Subtracting ar(BDM) from both the sides
ar(CBD) – ar(BDM) = ar(FBD) – ar(BDM)
⇒ ar(CMD) = ar(BFM)
Hence, in place of ΔCMD, if ΔBFM be given to Itwaari, his plot become triangular (ΔADF).