Computation of Areas

 

Computation of Areas

·       Generally, the lands will be of irregular shaped polygons.

·       There are formulae readily available for regular polygons like triangle, rectangle, square and other polygons.

·       But for determining the areas of irregular polygons, different methods are used.

·       Earth work computation is involved in the excavation of canals, digging of trenches for laying underground pipe lines, formation of bunds, earthen embankments, digging farm ponds, land levelling and smoothening.

·       In most of the computation the cross-sectional areas at different interval along the length of the channels and embankments are first calculated and the volume of prismoids are obtained between successive cross section either by trapezoidal (or) Prisimoidal formula.

·       Calculation of area is carried out by many of the following methods.

                          I.          Simpsons rule

                        II.          Boundaries with offsets at irregular intervals.

                      III.          Meridian methods

                      IV.          Co- ordinate method

 

Simpsons Rule:

In this rule, the boundaries between the ends of the ordinates are assumed to form an arc of parabola hence Simpsons rule is sometimes called as parabolic rule.

Let o₁, o₂, o₃ = Three consecutive ordinates

d= common distance between the ordinates.

Area of AFeDC= Area of AFDC(TRAPEZOID)+Area of FeDEF (SEGMENT)

Example:

The following offsets were taken from a chain line to an irregular boundary line at an interval of 10m

0,2.50,3.50,5.0,4.60,3.0,0m, calculate the area by Simpsons rule