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.
Please explain it with a diagrams
To implement this proposal, the Gram Panchayat needs to take over a portion of Itwaari's plot to construct a Health Centre. Let's refer to the quadrilateral plot as ABCD, where A, B, C, and D are the corners.
1. Determine the corner (let's say A) from where the Gram Panchayat plans to take over a portion of Itwaari's land to construct the Health Centre.
2. Now, to fulfill Itwaari's condition, the Gram Panchayat needs to provide an equal amount of land to Itwaari. This land should be adjacent to Itwaari's plot to form a triangular plot.
3. Draw a line from point A, bisecting the opposite side BC. Let's call the point of intersection E.
4. Draw a perpendicular line from point E to the side AD. Let's call the point of intersection F.
5. Now, draw a line from point F to point B. This will divide Itwaari's plot ABCD into two parts: the original quadrilateral plot ABCF and the new triangular plot ABF.
6. The new triangular plot ABF will be the equal area provided to Itwaari, fulfilling his condition.
Here is a diagram to help visualize the explanation:
C
/ \
/ \
/ \
/_______\
A E F B
\ /
\ /
\ /
\ /
D
In this diagram, the original plot ABCD is divided into the original quadrilateral plot ABCF and the new triangular plot ABF. The point E bisects the side BC, and the point F is the intersection of a perpendicular line from E to AD. The line FB creates the triangular plot ABF.