Question

Ram has a plot of land of the shape of a quadrilateral. Government wants to take some portion of his land to build a hospital. Ram agrees 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. [4 MARKS]

Answer 1

Diagram : 1 Mark
Concept : 1 Mark
Application of the concept: 1 Mark
Calculation : 1 Mark

Let quadrilateral ABCD be the shape of the field.

Join diagonal BD and draw a line parallel to BD through point A. Let it meet the extended side CD of ABCD at point E. Join BE.
BE and AD intersects each other at O.
Let portion $△$AOB can be cut from the original field for hospital purpose.

It can be observed that $△$DEB and $△$DAB lie on the same base BD and are between the same parallels BD and AE.

$\therefore$ ar ($△$DEB) = ar ($△$DAB)

$\Rightarrow$ ar ($△$DEB) − ar ($△$DOB) = ar ($△$DAB) − ar ($△$DOB)

$\Rightarrow$ ar ($△$DEO) = ar ($△$AOB)

So, the triangular plot of the area DEO is given to Ram by the government in lieu of the land obtained from his original quadrilateral plot.