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.

Given:

Ordinates

O1 = 10

O2 = 13

O3 = 17

O4 = 16

O5 = 19

O6 = 21

O7 = 20

O8 = 18

Common distance, d =10m

Number of equal parts of the baseline, n = 8

Length of baseline, L = n *d = 8*10 = 80m

Area = [(10+13+17+16+19+21+20+18)*80]/8

= 1340sqm