The renowned engineer, Parag Pal, explained the process for working out land area with triangulation in the folowing tutorial.
In surveying, triangulation is the process of determining the location of a point by measuring only angles to it from known points at either end of a fixed baseline, rather than measuring distances to the point directly as in trilateration. The point can then be fixed as the third point of a triangle with one known side and two known angles.
Triangulation can also refer to the accurate surveying of systems of very large triangles, called triangulation networks.
By applying trigonometry and the measured length of just one side, the other distances in the triangle are measured. The shape of the triangles is very crucial as there may be several errors in a long skinny triangle, but one having base angles of about 45 degrees is perfect.
Each of the distances already calculated is then applied as one side in another triangle to work out the distances to another point, which sequentially can set up another triangle.
As needed, it is performed frequently to develop a chain of triangles which connect the origin point to the Survey Control in the required place.
The angles and distances are then applied with the preliminary identified position, and complicated formulae, to calculate the position (Latitude and Longitude) of all other points in the triangulation network.
The calculated distance in the first triangle is called as the ‘Baseline’ and is the only distance measured; all the rest are computed from it and the measured angles.
The process is very simple to compute the area of right angle triangle, but in case the triangle is not right angle, the process becomes complicated. In the tutorial, given below, you will learn how to simplify this complicated process with the use of some formulas.
The process can be followed in surveying calculation.
To begin with, you have to calculate the coefficient of triangle “S”.
S = ½ x (a+b+c), here a,b,c represent three sides of the triangle. AB as first side, BC as second side and CA as third side. AB is represented as A, BC represented as B and CA represented as C. Their values are given as follow :-
AB = 5 meter, BC = 8 meter and C = 12 meter
By putting these values, we get S = ½ (5+8+12) = 12.5
Now land area can be worked out with the following formula, which will be presented in the video :