A villager It waari has a plot of land of the shape of a quadrilateral

1.	A villager It waari 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.
Answer» Let the shape of plot be quadrilateral ABCD. Itwaari agrees to give land as follows: Diagonal AC of a quadrilateral is joined. BA side of land ABCD is produced to E. CE and DE \|\| AC are drawn. Now, ∆ACD and ∆ACE are on same base aC and in between AC \|\| DE. ∴ ar.(∆ACD) = ar.(∆ACE) Subtracting ar.(∆AOC) on both sides ar (∆ACD) – ar(∆AOC) = ar(∆ACE) – ar(∆AOC) ar.(∆DOC) = ar.(∆AOC). Now, Itwaari agrees to give ADOC to construct a Health Centre. Area of ∆AOE and ∆CEB is remains with Itrwaari.

A villager It waari 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.

Answer»

Let the shape of plot be quadrilateral ABCD. Itwaari agrees to give land as follows:

Diagonal AC of a quadrilateral is joined. BA side of land ABCD is produced to E.

CE and DE || AC are drawn.

Now, ∆ACD and ∆ACE are on same base aC and in between AC || DE.

∴ ar.(∆ACD) = ar.(∆ACE)

Subtracting ar.(∆AOC) on both sides

ar (∆ACD) – ar(∆AOC) = ar(∆ACE) – ar(∆AOC)

ar.(∆DOC) = ar.(∆AOC).

Now, Itwaari agrees to give ADOC to construct a Health Centre.

Area of ∆AOE and ∆CEB is remains with Itrwaari.