Irregular Boundary Area

Curved or wavy boundary by offsets

Interval between offsetsOffset 1Offset 2Offset 3Offset 4Offset 5Offset 6Offset 7

Area

m²

Offsets used: 2 nos over 0 m
Trapezoidal rule: 0 m²
Simpson's rule: Needs an odd number of offsets
In square feet: 0 sq ft
In cents: 0 cents
Mean offset: NaN m

Mark

Quantitynos

How we got this

1
Set out the base line
Base length = Interval × (No. of offsets − 1)
= 0 × 1
= 0 m
2
End and intermediate offsets
Ends = O₁ + Oₙ ; Middles = O₂ + … + Oₙ₋₁
= Ends 0 + 0 = 0 · Middles = 0
= 0, 0 m
3
Trapezoidal rule
A = d/2 × [(O₁ + Oₙ) + 2(O₂ + O₃ + … + Oₙ₋₁)]
= 0/2 × [0 + 2 × 0]
= 0 m²
Treats the boundary between two offsets as a straight line — slightly under-reads a convex curve.
4
Simpson's one-third rule
A = d/3 × [(O₁ + Oₙ) + 4(even offsets) + 2(odd offsets)]
= 1 divisions — Simpson's rule needs an even number
= Add or drop one offset to use it
Fits a parabola through every three offsets, so it follows a curved boundary far more closely.
5
Area adopted
Adopt trapezoidal rule
= 0 m²
= 0 m² = 0 sq ft = 0 cents
Add this to the regular rectangular portion of the plot to get the total area.

The theory behind it

Method used: Trapezoidal rule and Simpson's rule on equally-spaced offsets — IS 1200 Part 1

When one boundary is curved — a road edge, a nala or a stream — run a straight survey line (base line) along the plot and measure perpendicular offsets to the boundary at equal intervals. The area between the base line and the boundary is then found by the trapezoidal rule, or more accurately by Simpson's one-third rule when the number of divisions is even.

Assumptions used

•Offsets are perpendicular to the base line and equally spaced.
•Enter 0 for any offset you did not take; unused offsets at the end are ignored.
•Simpson's rule is shown only when the number of divisions is even (odd number of offsets).
•Closer offsets give a better answer on a sharply curving boundary.

Codes & references

IS 1200 (Part 1):1992 — Measurement of areas
Surveying — trapezoidal and Simpson's one-third rules

History

Estimates for guidance only. Confirm quantities with your site engineer.