Methods used for the calculation of areas in Surveying

Methods used for the calculation of areas in Surveying:

1. Simpson’s rule
2. Trapezoidal rule
3. Graphical rule

Simpson’s Rule

Statement

It states that, sum of first and last ordinates has to be done. Add twice the sum of remaining odd ordinates and four times the sum of remaining even ordinates. Multiply to this total sum by 1/3^rd of the common distance between the ordinates which gives the required area.

Where O₁, O₂, O₃, …. O_n are the lengths of the ordinates

x = common distance

n = number of divisions

Note:

This rule is applicable only if ordinates are odd, i.e. even number of divisions.

If the number of ordinates are even, the area of last division maybe calculated separated and added to the result obtained by applying Simpson’s rule to two remaining ordinates.

Even if first or last ordinate happens to be zero, they are not to be omitted from Simpson’s rule.

The following offsets are taken from a chain line to an irregular boundary towards right side of the chain line.

0ffset	y1	y2	y3	y4	y5	y6	y7
magnitude	7	13	16	17	21	26	14

Common distance, x = 90m

Area = x/3[(O₁+O₇) + 2 (O₃+O₅)+4(O₂+O4+O₆)]

= 90/3[(7+14)+2(16+21)+4(13+17+26)]

Area = 9,570sqm





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