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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. |
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Answer» Two Triangles on the same BASE and between the same parallels are equal in area Let ABCD be the plot of the land of the shape of a quadrilateral. Construction, Diagonal BD is joined. AE is drawn parallel BD. BE is joined which INTERSECTED AD at O. △BCE is the shape of the original field and △AOB is the area for constructing health CENTRE. Also, △DEO land joined to the plot. To prove: ar(△DEO) = ar(△AOB) Proof: △DEB and △DAB lie on the same base BD and between the same parallel lines BD and AE. ar(△DEB) = ar(△DAB) ar(△DEB) – ar△DOB) = ar(△DAB) – ar(△DOB) [ On subtracting ar(△DOB) from both sides] ar(△DEO) = ar(△AOB) Hope this will HELP you... |
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