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User Comments
  Posted by Mircea LUTIC on February 1, 2005
The result of Area() depends on the type of Spatial Reference (SRID).

The value above is based on euclidian geometry.

The area of a triangle (and hence of a Polygon and MultiPolygon) is given by Heron's formula
SQRT ( s * (s-a) * (s-b) * (s-c) )
only in planar (euclidian) geometry.

Here a, b and c are the lengths of the sides of a triangle as given by GLength() (see also comment on MultiLineString functions) and s=(a+b+c)/2.

On a sphere where coordinates are lattitude and longitude and the lengths of the sides are measured in radians the formula to use for the area is

AreaInSteradians = 4*atan(sqrt( tan(s/2) * tan((s-a)/2) * tan((s-b)/2) * tan((s-c)/2) ))

AreaInSqMeters = AreaInSteradians * RadiusOfSphere^2

See also my comment on MultiLineString Functions
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