Math question: How to compute the area of polygons

[Gernot Lorenz]

Malte Brill wrote:

>Hi List,
>
>
>this one goes out to the math experts.
>How does one compute the area ( I hope it is the correct Term for
>flaecheninhalt in german) of a polygon with n sides.
>
>(That would get me started.)
>
>I want to extract all lines of 2 polygons by analysing their points,
>evaluate the area of each of them with some magic formula I don´t know ;-)
>and to figure out the area of the smallest polygon surrounding both of them.
>
>  
>
Hallo Malte,
wenn sich das Polygon nicht schneidet, geht es folgendermaßen: Es wird 
in Dreiecke zerlegt (man nimmt ein Polygonpunkt und verbindet ihn mit 
allen anderen); angenommen, die Koordinaten der 3 Eckpunkte sind 
(ax,ay), (bx,by) und (cx,cy) dann gilt für den Flächeninhalt: F = 
[ax*(by - cy) + bx*(cy - ay) + cx*(ay - by)]/2.
Diese Berechnung muß nun für alle entstandenen Dreiecke durchgeführt und 
die Ergebnisse addiert werden.
In English:
If the polygon does not cross itself, the following method helps: the 
polygon has to be divided into triangulars (choose one point of the 
polygon and connect it with all the others); supposed, the coordinates 
of the three triangular points are (ax,ay), (bx,by) und (cx,cy), then 
the area F will be calculated with [ax*(by - cy) + bx*(cy - ay) + cx*(ay 
- by)]/2.
This has to be done for all the triangulars and the areas have be added 
and give the total area.
( I know, bad English from "old Europe")

Gruß
Gernot

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