A villager Itwari has a plot of land of the shape of a quadrilateral. The Gram Panchayat of the village decided to take over some portion of plot from one of the corners to construct a Health centre. Itwari 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 his proposal will be implemented.

Explanation

Solution
Construction
Join diagonal `BD`.
Draw `AE` parallel to `BD`.
Join `BE`, that intersected `AD` at `O`.
By construction
We get,
`/_\BCE` is the shape of the original field
`/_\AOB` is the area for constructing health centre.
`/_\DEO` is the land joined to the plot.
Now,
`/_\DEB` and `/_\DAB` lie on the same base `BD`, in-between the same parallels `BD` and `AE.`
Hence,
`ar(/_\DEB) = ar(/_\DAB)`
`=> ar(/_\DEB) – ar(/_\DOB) = ar(/_\DAB) – ar(/_\DOB)`
`=> ar(/_\DEO) = ar(/_\AOB)`.