Question

A villager Ramayya has a plot of land in the shape of a quadrilateral. The grampanchayat of the village decided 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.​

Answer 1

Let ABCD is the quadrilateral plot of Itwari.

Draw Diagonal BD and CE || BD. Now join DE which intersects BC at point O.

Now from figure,

ΔBDE and ΔBDC have the same base BD and between the same parallels BD and CE

So   Area(ΔBDE) = Area(ΔBDC)

Now subtract Area(ΔBDO) on both side, we get

=> Area(ΔBDE) - Area(ΔBDO) = Area(ΔBDC) - Area(ΔBDO))

=> Area(ΔCOD) = Area(ΔBOE)

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