A villager Itwaari 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.
Let's suppose that villager has land in the form of quadrilateral ABCD. Let's suppose that the Gram Panchayat takes some part of his land from the corner B. To solve his problem, other part of land will be given to him adjoining his land. The final shape of his plot needs to be triangular and the area of final plot should be equal to area of quadrilateral ABCD.
Let's join AC. Through B draw a line parallel to AC meeting DC at E. Finally join AE.
We can clearly see that and are on the same base AC and between the same parallels BE and AC.
(Triangles on the same base and between the same parallels are equal in area.)
It means that area of quadrilateral ABCD is equal to area of . So, the Gram Panchayat can take away triangular part AOB and can give him triangular part COE. The final shape of his plot will be triangular and it will be equal to the area of quadrilateral ABCD.