Determination of areas by dividing the area into a number of triangles

BY DIVIDING THE AREA INTO A NUMBER OF TRIANGLES

See Fig. 45. The given area is divided into a number of triangles. The area of each triangle is determined. The sum of the areas of all the triangles within the figure is the total area.

The sides of the triangle are measured. If a, b, c are the lengths of the sides of a triangle, the area of the triangle =

Aliter: Area of the ∆ AOB can also be determined by measuring the lengths OA and OB and the included angle AOB using a Theodolite.

i.e., Area of ∆ AOB  = 1/2 × (Product of two sides × Sine of included angle)

= 1/2 × (OA × OB) × Sine ∠AOB