## Methods of Calculation of Areas in Surveying | Simpson’s Rule

#### 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 1/3rd of the common distance between the ordinates which gives the required area.

Where O1, O2, O3, …. On 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.

## Methods for Calculation of Areas in Surveying | Average Ordinate Rule

#### Calculation of Areas in Surveying | Average Ordinate Rule

In one of my previous articles, I discussed Midpoint 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) 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

#### Average Ordinate Rule

The rule states that (to the average of all the ordinates taken at each of the division of equal length multiplies by baseline length divided by number of ordinates).

O1, O2, O3, O4….On ordinate taken at each of division.

L = length of baseline

n = number of equal parts (the baseline divided)

d = common distance

#### Area = [(O1+ O2+ O3+ …. + On)*L]/(n+1)

Here is an example of a numerical problem regarding the calculation of areas using Average Ordinate Rule

## Different Methods for the Calculation of Areas in Surveying

#### Different methods for the calculation of Areas in the field of Surveying

In this article, we will list out different methods to calculate the areas in Surveying and also study each of the method in depth… We will also explain each method with a suitable example for your better understanding…

#### 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

We will now move on with our discussion on the first rule “Midpoint ordinate rule” with a suitable example.

#### Midpoint-ordinate rule

The rule states that if the sum of all the ordinates taken at midpoints of each division multiplied by the length of the base line having the ordinates (9 divided by number of equal parts).

In this, base line AB is divided into equal parts and the ordinates are measured in the midpoints of each division.

Area = ([O1 +O2 + O3 + …..+ On]*L)/n

L = length of baseline

n = number of equal parts, the baseline is divided

d = common distance between the ordinates

#### Example of the area calculation by midpoint ordinate rule

The following perpendicular offsets were taken at 10m interval from a survey line to an irregular boundary line. The ordinates are measured at midpoint of the division are 10, 13, 17, 16, 19, 21, 20 and 18m. Calculate the are enclosed by the midpoint ordinate rule.