9 land area determination

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Land Area

Determination

Florence A. GaleonAssistant Professor

U.P. College of Engineering


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Outline

I. Introduction

II. Methods of Determining Land Area

III. Rules in Computing DMD

IV. Sample Problem and Solution

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Introduction

Area determination is one of the primaryobjectives of land surveys.

Area is a final determinant of the totalmarket value of a piece of land put on

sale to the public.

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Methods of Determining Land Area

1. Area by Triangles

The area can be found by dividing thelot into a series of triangles, making thenecessary measurements and then

calculating the area by any of the usualtrigonometric formulas.


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Area by Triangles Formula

A = a.b sinC

A = s(s-a)(s-b)(s-c)

where s = (a+b+c)

Area by Triangles

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2. Area by Coordinate Squares

The scaled drawing is marked off insquares of unit areas then counted. Thisis used to approximate areas.


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Coordinates Squares Illustration


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3. Area by Polar Planimeter

The polar planimeter is a mechanicaldevice used to determine the area of anyshape of figure plotted to a known scale

by directly tracing the perimeter andreading the result from the scale.


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Parts of a Polar Planimeter


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Sample Polar Planimeters


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4. Area by Offsets from Straight Lines

Areas with irregular or curved boundaries areusually measured by establishing a base lineconveniently near and by taking offsets at regularintervals from the base line to the boundary.

4.1 Trapezoidal Rule4.2 Simpsons One-Third Rule


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Trapezoidal Rule Illustration


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Illustrative Problem


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Illustrative Problem


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5. Area by Coordinates

The method of coordinates is based on thefollowing rule in analytic geometry: If the verticesof the figure are taken in order around thefigure, the area is equal to one-half the sum of

the products of each ordinate multiplied by thedifference between the two adjacent abscissasalways subtracting the preceding from thefollowing abscissa.


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Area Calculation by Coordinate Method


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Area Calculation by Coordinate Method

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EastingsNorthings

EastingsNorthings


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6. Area by Double Meridian DistanceMethod

Meridian distance is the distance of themidpoint of a line to the reference meridian.

This method is an adaptation of thecoordinates method and is convenient to usewhen the latitudes and departures of thetraverse are known.


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DMD Illustration


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Rules in Computing DMD

1. The DMD of the first line is equal to thedeparture of that line.

2. The DMD of any other line is equal to theDMD of the preceding line, plus the

departure of the preceding line, plus thedeparture of the line itself.

3. The DMD of the last line is numericallyequal to the departure of the line but withopposite sign.


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Sample Problem

LINE LAT DEP

1-2 + 10.49 + 8.76

2-3 - 12.66 + 11.30

3-4 - 15.23 + 13.484-5 - 7.05 - 27.19

5-1 + 24.45 - 6.35

Given the following data of a balanced closedtraverse, determine the area by DMD Method.


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Sample Problem Solution

LINE LAT DEP DMD DA

1-2 + 10.49 + 8.76

2-3 - 12.66 + 11.303-4 - 15.23 + 13.48

4-5 - 7.05 - 27.19

5-1 + 24.45 - 6.35

2A = ______

A = ______


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Sample Problem Solution

LINE LAT DEP DMD DA

1-2 + 10.49 + 8.76 + 8.76 + 91.89

2-3 - 12.66 + 11.30 + 28.82 - 364.863-4 - 15.23 + 13.48 + 53.60 - 816.33

4-5 - 7.05 - 27.19 + 39.89 - 281.22

5-1 + 24.45 - 6.35 + 6.35 + 155.26

2A = - 1215.26

A = 607.63 m


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9 land area determination

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