Calculation of Areas in Surveying | Simpson’s Rule

In one of my previous articles, I discussed Midpoint Ordinate Rule and Average Ordinate Rule in detail with an example and listed out various important methods used for the calculation of areas in Surveying. In this article, we will deal with the next important method (rule) i.e. Simpson’s Rule along with a numerical example used for the calculation of areas in the field of Surveying.

Here are the five important rules (Methods) used for the calculation of areas in Surveying:

1. Midpoint ordinate rule
2. Average ordinate rule
3. Simpson’s rule
4. Trapezoidal rule
5. Graphical rule

Simpson’s Rule

Statement

It states that, sum of first and last ordinates has to be done. Add twice the sum of remaining odd ordinates and four times the sum of remaining even ordinates. Multiply to this total sum by 1/3^rd of the common distance between the ordinates which gives the required area.

Where O₁, O₂, O₃, …. O_n are the lengths of the ordinates

d = common distance

n = number of divisions

Note:

This rule is applicable only if ordinates are odd, i.e. even number of divisions.

If the number of ordinates are even, the area of last division maybe calculated separated and added to the result obtained by applying Simpson’s rule to two remaining ordinates.

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