Well why would it be impossible? The approach I would try would be to break an n-pointed star into 2n triangles. Choose some point and call it the center (the choice should ensure that your figure is star convex about the point). Each of your triangles should have this center as a vertex. Every point should be a vertex of two different triangles, so every line segement which joins a point to the center is an arm shared by two triangles. The sum of the areas of the triangles is the area of the star.
EDIT: Rather than using [itex]\LaTeX[/itex], you could (and this would work better anyways, I think) draw a picture in Paint and upload it as a .jpg file.
I can form a value for it given certain information, but you haven't given me any information. Give me an example of a star and I'll show you how to compute it's area using the technique above. There may be some ways of the defining the star such that the given information makes it difficult to use the technique above, but if, for example, you define the star for me by giving me the co-ordinates of all the "outer" points and all the "inner" points, it will be very easy.
Are you referring to area in a general form, i.e. equation or just one particular instance? If just one instance, you'll have 5 triangles and a pentagon. Sum all of the individual areas. A picture would be nice just to make sure though.
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