A villager ramayya has a plot of land in the shape of a quadrilateral.

1.	A villager ramayya has a plot of land in the shape of a quadrilateral.The grampanchayat of the village decide to take over some portion of his plot from one of the corners to construct a school. Ramayya agrees to the above proposal with the condition that he should be given equal amount of land in exchange of his land adjoining his plot so as to form a triangular plot.Explain how this proposal will be implemented.(draw a rough sketch of plot).
Answer» Step-by-step explanation: ⇒ Let ABCD is the quadrilateral plot of Rammaya. ⇒ Draw diagonal BD and CE\paralle$$BD. Now, join DE which intersects BC at point O. ⇒ Now from figure, ⇒ △BDE and △BDC have the same base BD and between the same PARALLELS BD and CE. ⇒ So, AREA(△BDE)=Area(△BDC) ⇒ Now subtract $$Area(\TRIANGLE BDO) on both sides, we get ⇒ Area(△BDE)−Area(△BDO)=Area(△BDC)−Area(△BDO) ⇒ Area(△COD)=Area(△BOE) SoRammayacandisposeArea(△COD)fromhisplotABCDandgetArea(△BOE)inadjacentandthen hewillhaveatrianglelandADE.

A villager ramayya has a plot of land in the shape of a quadrilateral.The grampanchayat of the village decide to take over some portion of his plot from one of the corners to construct a school. Ramayya agrees to the above proposal with the condition that he should be given equal amount of land in exchange of his land adjoining his plot so as to form a triangular plot.Explain how this proposal will be implemented.(draw a rough sketch of plot).

Answer»

Step-by-step explanation:

⇒ Let ABCD is the quadrilateral plot of Rammaya.

⇒ Draw diagonal BD and CE\paralle$$BD. Now, join DE which intersects BC at point O.

⇒ Now from figure,

⇒ △BDE and △BDC have the same base BD and between the same PARALLELS BD and CE.

⇒ So, AREA(△BDE)=Area(△BDC)

⇒ Now subtract $$Area(\TRIANGLE BDO) on both sides, we get

⇒ Area(△BDE)−Area(△BDO)=Area(△BDC)−Area(△BDO)

⇒ Area(△COD)=Area(△BOE)

SoRammayacandisposeArea(△COD)fromhisplotABCDandgetArea(△BOE)inadjacentandthen

hewillhaveatrianglelandADE.