Nice code Gilles, just want to say that if performance is important, you don't need to divide by 2 the area, just the sign matters for the test, may be I'm wrong, but I think the same apply for arcs, it doesn't matter the area of them just the start and end point order.
I know that, but as these extension methods may be reusable, I prefered let them return the right area.
About performance issue, I think (without testing) this won't be sensible until you're looping through many polylines having a great number of vertices...
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