Page 3 of 3
3. Area Computation
The area of a noncrossing closed polygon, Figure C5,
Figure C5 Polygon Areas 
can be computed using the coordinates of its vertices:
Equation C5 
In surveying terms using North and East coordinates:
Equation C6 
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. 

Cross multiply.


Sum crossproducts 
Add the cross multiplication sums, divide by two, and take the absolute value to obtain the area:
Equation C7 
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.