Earthwork - Area by coordinates

[maximus808]

Can someone help explain how to calculate Area by Coordinates:

Here's the formula: Area=Xa(Yb-Yn)+Xb(Yc-Ya)+Xc(Yd-Yb)......../2

Maybe a picture/diagram or anything will be helpful. Thanks.

 

[EM_PS]

So you have coordinate values; something like

X1, X2, X3...Xi and Y1, Y2, Y3...Yi

Easiest way is to form 2 columns for the X & Y values, and repeat the X1, Y1 values at bottom (closes the polygon loop).

The formula is then [(X1*Y2 + X2*Y3 + ... Xi*Y1) - (Y1*X2 + Y2*X3 + ...Yi*X1)] *1/2

Obviously if you have a negative number take the absolute value. Youre simply summing the cross multiplication of the row 1 * row 2 (and so on) values, for both columns, subtracting the two summations, and dividing by 2.

The formula in the FS manual is Area= 1/2 [∑ Xi*Y(i+1) -∑ Xi*Y(i-1) ]

Where ί is point order in a closed polygon. Same general procedure.

 

[Badger]

Maybe this will help.

find_area.pdf

 

[civilized_naah]

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