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Finding the area of a geopolygon (made of longitude latitude points)

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How would you go about, or does anyone know of any articles/references on calculating the area of a polygon? (Remember that maps are distorted towards the poles, to the actual area isn't just the polygon area) Or any suggestions on how I might go about calculating this?

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This link http://mathforum.org/library/drmath/view/63767.html

 

gives a formula for calculating a latitude/longitude rectangle area (i.e. between 2 lines of longitude and 2 lines of latitude).

 

The formula it gives is

 

A = 2*pi*R^2 |sin(lat1)-sin(lat2)| |lon1-lon2|/360
    = (pi/180)R^2 |sin(lat1)-sin(lat2)| |lon1-lon2|

 

Working it out for arbitrary polygons might be trickier...

 

EDIT: sin function there is the degrees sin function so convert the latitude to radians (longitude stays as degrees).

 

EDIT2: I also found something about working out the area of a spherical triangle defined with great circles, I can post that if you want, but lines of latitude are not great circles (except the Equator) so I'm guessing that's not what you want...

Edited by Paradigm Shifter

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Yeah, I'm working with arbitrary polygons. I think the better approach is converting between projections. I found a number of projections called equal-area projections that means that the polygon area is correct because points near the poles are closer together vertically.

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