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.
Answers
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...
Answer:
Let quadrilateral ABCD be the original shape of the field owned by Itwaari
Let us join AC and draw DE ll AC
Joining CE and EA