1.16.7.a. Computation of areas

The land is always dealt with area. For any engineering project, land is acquired first on the basis of area requirement. In some projects, land may be required along a corridor of defined width (e.g., rail, road, pipeline etc.), while in other projects a large catchment area may be involved, such as flood protection devices, reservoir, etc.). Thus, determining the requirement of area in a project is an essential part of surveying.

In engineering projects, understanding how much land is needed is crucial. This 'area requirement' can differ significantly based on project types. For example, a rail line may need a narrow strip of land, while a reservoir may encompass a large area to hold water. Surveying helps measure this land accurately before any development starts.

Consider planning a park. If you want a playground (small area), you only need a small part of land. But if you plan for a lake and picnic areas, you'll need much more land. Understanding these area needs is like creating a recipe—knowing how much space you need for each component.

It is very easy to determine the area of a regular figure (plot of land), such as a triangle, a square, a rectangle, etc. However, most of the time, the project land is irregular in shape with no defined shape, so computation of area is not straight forward in such cases.

For simple shapes like rectangles or triangles, calculating area is straightforward. However, most land shapes are irregular, making calculation more complex. For example, consider a plot with a curved edge. This requires special methods to accurately estimate its area.

Imagine you want to calculate the area of a garden that isn't perfectly square; it has curves and corners. It's like measuring the amount of paint you need for an oddly shaped room. You can't just multiply length and width; you need to break it down into manageable parts.

For this purpose, from a survey line offsets are taken at regular intervals, and area is calculated from any of the following methods: (i) Trapezoidal rule (ii) Simpson’s rule (iii) Using planimeter (iv) From coordinates

To manage the complexity of irregular shapes, several methods are available for area computation. These involve taking measurements along a survey line at set intervals. Methods range from geometrical calculations like the trapezoidal and Simpson’s rules to using specialized tools like a planimeter or mathematical coordinate systems. Each method has its application based on the shape and requirements of the land.

Think of each method like different tools in a toolbox. Just as you might use a hammer for nails but a wrench for bolts, you select your method based on the shape and complexity of the area you want to measure.

In trapezoidal rule, the area is divided into a number of trapezoids, and boundaries are assumed to be straight between pairs of offsets. The area of each trapezoid is determined and added together to compute the entire area.

The trapezoidal rule simplifies area calculation by approximating irregular shapes as a series of trapezoids. Each trapezoid's area can be calculated straightforwardly and then summed up to find the total area. This method assumes that straight lines connect the measurement points for precise estimations.

Imagine laying out a garden bed that is uneven. Instead of trying to measure every curve, you can outline sections as rectangles and trapezoids. Calculate the area for each section, then add them together, making it easier than trying to calculate the whole shape's area at once.

In Simpson's rule, it is assumed that the irregular boundary is made up of parabolic arcs. The areas of the successive pairs of intercepts are added together to get the total area.

Simpson's rule is an advanced method that models irregular boundaries as smooth curves (parabolic arcs). This approach provides a more accurate area calculation for complex shapes. Like the trapezoidal rule, it involves dividing the area but adds a layer of sophistication by accounting for the curve's nature.

Consider a riverbank that curves as you measure its width at different points. Using Simpson’s rule is like tracing that curve smoothly rather than just measuring straight across; it gives you a better idea of the area along the bank's shape.

Planimeter is a mechanical instrument used for measuring the area of a plan. It consists of a hard steel roller and a disc. To find the area from a map, the anchor pin of the planimeter is placed either outside or inside the map.

A planimeter is a practical tool designed for measuring areas directly from maps. It operates by tracing the perimeter of the area, and its mechanical dials record the area in square units. The anchor pin's position—inside or outside the shape—determines how effectively the tool captures the entire area.

Think of a planimeter like a mechanical pencil drawing the outline of a cookie. As you trace around it, the pencil measures how much cookie dough the shape would need. Similarly, a planimeter traces and measures land shapes to find their area.

The area of an irregular closed polygon is usually computed by the coordinate method. In this procedure, coordinates of each turning point in the figure must be known.

The coordinate method involves using the GPS coordinates of each corner of an irregular shape to calculate its area. By applying a specific mathematical formula that takes these coordinates, surveyors can derive the total area accurately. This method is ideal for technology-based measurements.

Imagine you’re marking the corners of a park with GPS on your phone. Once you've saved all the points, the app can tell you how big the park is by processing those coordinates, just like this method does for measuring land area.

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