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Calculating Areas Using Double Meridian Distance and Triangular Coordinates Methods, Quizzes of Survey Sampling Techniques

San Francisco State University (SFSU)Survey Sampling Techniques

A detailed explanation of two methods for calculating areas: the double meridian distance (dmd) method and the triangular coordinates method. It outlines the steps involved in each method, including formulas and examples. The document also includes a homework assignment that requires students to apply the dmd method to calculate the area of a traverse.

Typology: Quizzes

2021/2022

Uploaded on 03/01/2025

talop-shah
talop-shah 🇺🇸

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5/2/2017
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Calculating Areas:
There are many methods for
calculating areas
Such as
1. Dividing the area into rectangles and
triangles
2. Dividing the area into triangles
Each n-sided traverse can be divided into (n-2)
trangles
3. Dividing the area into grids (counting the grids
and multiplying the numbers by the area of
one grid)
pf3
pf4
pf5

Partial preview of the text

Download Calculating Areas Using Double Meridian Distance and Triangular Coordinates Methods and more Quizzes Survey Sampling Techniques in PDF only on Docsity!

Calculating Areas:

There are many methods for

calculating areas

Such as

  1. Dividing the area into rectangles and triangles
  2. Dividing the area into triangles Each n-sided traverse can be divided into (n-2) trangles
  3. Dividing the area into grids (counting the grids and multiplying the numbers by the area of one grid)
  1. Using a tool called planimeter. It determines the area by tracing the perimeter of the area.

Mechanical Planimeter Electronic Planimeter

The 2 Most Practical Methods

  1. Double Meridian Distance
  2. Triangular Coordinates Methods

Double Meridian Distance

  • Meridian Distance of a line: Distance parallel to the E-W direction from the reference N-S meridian to the mid point of the line
  • Double Meridian Distance: Double the meridian distance!

General Rule (DMD Method)

  • DMD of first line: DMD= Dep of this line
  • DMD of any line: DMDij = DMDhi+Dephi+Depij
  • Area = ½ S DMD * Lat for all lines

Example

Lines Azimuth Side Dist (ft) (degrees) Dept Lat AB 102.494 350.884 -16.2567238 101. BC 256.841 265.393 -256.008087 -20. CD 182.105 88.591 182.049669 4. DA 123.971 133.316 90.20547 -85. Lines Azimuth Side Dist (ft) (degrees) Dept Lat AB 102.494 350.884 -16.2567238 101. BC 256.841 265.393 -256.008087 -20. CD 182.105 88.591 182.049669 4. DA 123.971 133.316 90.20547 -85. Dep Lat DMD Double Area AB -16.24 101.20 528.26 53459. BC -256.01 -20.64 256.01 -5283. CD 182.05^ 4.49^ 182.05 816. DA 90.20 -85.05 454.30 -38637. SUM 0.00 0.00 10355.

  • Area = 10,355.28 / 2 = 5,177.64 SF

Triangular Coordinates Method

Obtain the coordinates of all the traverse points Then, apply the equation on the next slide

Theory General Rule

  • Each y-ordinate is multiplied by the difference between the two adjacent x-coordinates using a consistent sign notation such as +ve for the “following” and – ve for the “preceding.”

In Formula Form

Area = ½ S Yi * [Xi- 1 – Xi+1] for all i

Can also be written as

Area = ½ S Xi * [Yi- 1 – Yi+1] for all i

Example