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3. Area Computation

The area of a non-crossing closed polygon, Figure C-5,

img91a
Figure C-5
Polygon Areas

 

can be computed using the coordinates of its vertices:

img91bnew        Equation C-5

 

In surveying terms using North and East coordinates:

img91cnew        Equation C-6

 

An easy way to remember either equation is graphically:  

  X & Y E & N

List coordinates in order around exterior.

Repeat first coordinate pair at end.

img92ab img92bb

Cross multiply.

 

 

img92a img92b
Sum cross-products img98b

 

 Add the cross multiplication sums, divide by two, and take the absolute value to obtain the area:

img98a       Equation C-7

 

The absolute value is used because area could be positive or negative depending on traverse configuration, direction around it, and coordinate order (eg, E & N or N & E). Positive or negative, the area magnitude will be correct.

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