Short Answer:
The methods used to calculate the area in surveying depend on the shape of the land and the available measurements. For simple shapes like rectangles and triangles, basic geometric formulas are used. For irregular plots, techniques like the trapezoidal rule, Simpson’s rule, and planimeter are applied.
Surveyors also use coordinate methods where the boundary points are plotted with known coordinates and the area is calculated using mathematical formulas. These methods help in determining land sizes accurately for construction, planning, and legal purposes.
Detailed Explanation:
Methods used to calculate the area in surveying
Area calculation in surveying is a key task when determining the size of a plot or piece of land. This is important in land ownership records, construction, farming, and town planning. Since land parcels can be regular or irregular in shape, different methods are used based on the shape, accuracy required, and tools available.
Some methods are simple and use basic geometry, while others involve advanced calculations using coordinates or graphical tools. Below are the most commonly used methods.
1. Geometrical Method
This method is suitable for regular shapes like rectangles, triangles, and trapezoids. It uses basic area formulas:
- Rectangle: Area = length × breadth
- Triangle: Area = ½ × base × height
- Trapezoid: Area = ½ × (sum of parallel sides) × height
This is the most basic and quick method for simple plots.
2. Trapezoidal Rule
Used for irregular plots where sides are measured at regular intervals. The area is divided into several trapezoids. Formula:
Area = (d/2) × [first reading + last reading + 2(sum of intermediate readings)]
Where d is the distance between the measured points. This method works well for slightly curved or uneven plots.
3. Simpson’s Rule
This rule is used when the boundary is more curved. It divides the area into segments and applies a parabolic approximation.
Area = (d/3) × [first reading + last reading + 4(sum of odd readings) + 2(sum of even readings)]
Simpson’s rule gives more accurate results than the trapezoidal rule for curved boundaries.
4. Planimeter Method
A planimeter is a mechanical or digital instrument that measures the area of a closed figure on a map or plan. It is used when a scaled drawing is available. The planimeter is moved around the boundary, and it directly shows the area.
This method is fast and reliable when working with printed maps or layouts.
5. Coordinate Method (Double Meridian Distance or DMD method)
When the boundary points of a plot are known in coordinates (x, y), the area can be calculated using:
Area = ½ × |Σ(x₁y₂ − x₂y₁)|
This formula adds and subtracts products of coordinates and is useful in digital surveying or GPS-based methods.
6. Graphical or Grid Method
In this method, the area is drawn on graph paper with a fixed scale. The number of squares covered by the shape is counted, and the total area is estimated. It is a rough method used for visual estimation.
Conclusion
There are several methods used to calculate area in surveying, each suitable for different situations. For regular shapes, geometry-based formulas are used. For irregular land, methods like trapezoidal and Simpson’s rules provide better accuracy. Planimeters and coordinate methods are useful in modern surveying for precise and efficient area measurement.