## 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).

Average Ordinate Rule

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

The following perpendicular offsets were taken at 10m interval from a survey line to an irregular boundary line.

9, 12, 17, 15, 19, 21, 24, 22, 18

Calculate area enclosed between the survey line and irregular boundary line.

Area = [(O1+ O2+ O3+ …. + O9)*L]/(n+1)

= [(9+12+17+15+19+21+24+22+18)*8*10]/(8+1)

= 139538sqm

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