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Calculation of Area of Land

1) The document describes several methods for calculating the area of irregularly shaped land, including using offsets from a survey line to break the area into trapezoids and triangles. 2) Common methods include using mid-ordinate rules to draw ordinates at regular intervals along a baseline and calculating area, and trapezoidal rules which assume the area between ordinates forms trapezoids. 3) Calculating the area of a closed traverse can be done from field note coordinates using areas from coordinates, double meridian distances, or total latitudes and departures.

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Uchechukwu Marizu
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94 views10 pages

Calculation of Area of Land

1) The document describes several methods for calculating the area of irregularly shaped land, including using offsets from a survey line to break the area into trapezoids and triangles. 2) Common methods include using mid-ordinate rules to draw ordinates at regular intervals along a baseline and calculating area, and trapezoidal rules which assume the area between ordinates forms trapezoids. 3) Calculating the area of a closed traverse can be done from field note coordinates using areas from coordinates, double meridian distances, or total latitudes and departures.

Uploaded by

Uchechukwu Marizu
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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CALCULATION OF AREA OF LAND

One of the primary objective of most land surveys


in large scale surveying is to determine the area of
a tract.
A technique called traverse is run, the lines of the
traverse being made to coincide with property lines
where possible.
The length and bearing of all straight boundary lines
are determined either directly or by computation.
In case of irregular boundaries which are located
with respect to traverse line, perpendicular offsets
are taken at appropriate intervals and the radii and
central angles of circular boundaries are obtained.
GENERAL METHODS OF DETERMINING AREA

The followings are the general methods for calculating areas:-


• By computations based on directly on the field
measurement. These includes:
1. by dividing the area into a number of triangles
2 by offset to the base line
3 by latitude and departure
4 by double meridian ( DMD) method
5 By double parallel distance
6 By coordinates
7 By mechanical methods ( planimeter, pantographs etc.
Measurement of Area- Irregular Boundaries

Mathematical Rules : Here only common and popular


methods are illustrated for this course.
1. Area Between the Survey Lines and the Boundaries: - the
number of offsets are measured from the Survey line to the
nearest boundary line.
The area of the belts bounded by the adjacent offsets, the
boundary line and the base line may be assumed as trapeziums
and their area may be computed as under:
The area is calculated by multiplying the mean of each
successive pair of adjacent offsets, by the distance between
Them.
Mid Ordinate Rules : - in this method a baseline
AB is divided into a number of equal parts and
ordinates are drawn at the mid- points of each
division. The length of each ordinate is then
scaled off.
Area = Sum of the mid ordinates multiplied by
the common distance ‘d’
The Trapezoidal Rules : - in this method , a base line
AB is drawn and is divided into equal parts. The
ordinates at each point of division are drawn and their
lengths scaled off. This method assumes that the area
between adjacent ordinates is of the shape of a
trapezoid.
Example
The following perpendicular offsets were taken at 10 m interval
from a survey line AB to an irregular boundary lines,

10 10 10 10 10 10 10 10 B
A

2.50,3.50,4.5,6.5,5.2,7.5,8.8,8.3 and 5.5 metres. Calculate the


area in sq. m enclosed between the survey lines and the irregular boundary.
The first and the last offsets by Trapezoidal rules.
( Formula: A rea = d/2( first offests + last offest+2xsum of remaining offsets)
• CALCULATION OF AREA OF A
CLOSED TRAVERSE FROM
CO-ORDINATES
• The area of a closed traverse from field notes,
may be calculated by one of the following
methods;
• Areas from Coordinates
• Areas from Latitudes and Double Meridian
Distances
• Areas from Departure and Total Latitudes.
Area from Departure and Total Latitudes-

Assume any one of station as reference station from which the


Total latitude of the other station may be calculated.
• Rules:
• Calculate the total departure.
• Calculate the algebraic sum of the departures of the lines
meeting at that station.
• Multiply total latitude of each station by corresponding
algebraic sum of the departure.
• Calculate the algebraic sum of the product
• Half the sum gives the required area of the closed
traverse.
Example

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