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.

Question

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

Answer 1

To implement this proposal, the Gram Panchayat will need to ensure that Itwaari is given an equal amount of land in the form of a triangular plot adjoining his existing plot. Here's how it can be done:

1. Determine the area of the quadrilateral plot: The Gram Panchayat needs to calculate the area of Itwaari's existing quadrilateral plot.

2. Divide the area in half: Since Itwaari wants an equal amount of land in the form of a triangular plot, the Gram Panchayat needs to divide the calculated area of the quadrilateral plot into two equal parts.

3. Draw a line inside the quadrilateral: Based on the division of the area, the Gram Panchayat should draw a straight line from one corner of the quadrilateral to another, creating two triangular plots.

4. Construct the Health Centre: The Gram Panchayat can now use one of the created triangular plots to construct the Health Centre.

5. Allocate the new plot to Itwaari: The remaining triangular plot should be allocated to Itwaari as per his condition. This will ensure that he receives an equal amount of land in lieu of the portion taken for the Health Centre.

Here is a diagrammatic representation of the proposal:

```
Existing Quadrilateral Plot Dividing Line
_________________________ /
| | /
| | /
| | /
| | /
|_________________________| /
Triangular Plot 1 <------------/ Health Centre
(for Itwaari)

Triangular Plot 2
(for Itwaari)
```

In the diagram, the original quadrilateral plot is divided by a dividing line, creating two triangular plots. The Health Centre is constructed within one of the triangular plots, while the other triangular plot is allocated to Itwaari.