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, we need to consider the following steps:
Step 1: Understand the shape and dimensions of Itwaari's original plot. Let's assume Itwaari's original plot is a quadrilateral, and the dimensions of the sides are known.
Step 2: Determine the corner from which the Gram Panchayat wants to take over a portion of the land to construct the Health Centre. Let's assume this corner is labeled as "A."
Step 3: Calculate the area of Itwaari's original plot. This can be done using various methods, such as dividing the quadrilateral into triangles and calculating their individual areas or using more complex methods like Brahmagupta's formula or the shoelace formula. For the sake of simplicity, let's assume we calculate it using the triangle method.
Step 4: Divide the calculated area of Itwaari's original plot by 2 to obtain the desired area for the triangular plot that Itwaari will receive in lieu of the land taken by the Gram Panchayat.
Step 5: Identify the adjacent side of Itwaari's original plot that will be used to form the new triangular plot. Let's assume this adjacent side is labeled as "BC."
Step 6: Divide the desired area of the triangular plot obtained in Step 4 by the length of the adjacent side "BC" to obtain the height of the new triangular plot.
Step 7: Draw a perpendicular line from side "BC" at the endpoint "C" to represent the height of the new triangular plot. Ensure that the length of this perpendicular line corresponds to the height obtained in Step 6.
Step 8: Connect the endpoint of the perpendicular line ("D") to the vertex of the original plot where the land was taken over ("A"). This will form the boundary of the new triangular plot.
Step 9: Verify the dimensions of the newly formed triangular plot to ensure that its area indeed matches the desired area obtained in Step 4.
The diagram provided at the following link illustrates these steps: [Diagram](https://i.stack.imgur.com/I8kOx.png)
Please note that the above steps and the corresponding diagram are based on the assumption that Itwaari's original plot is a quadrilateral and the desired new plot is a right-angled triangle. The precise calculations and shape may vary depending on the specific dimensions and requirements of the scenario.