Aaron Tovish
Jan 21, 2025

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[Disclaimer: I am not a member so I could only read the first few paragraphs of this piece. Apologies in advance if I am discussing something already covered by it. AT]

Why not inscribe the triangle in x-y-oriented rectangle, and then subtract that areas of the right triangles. (One of the points will be in a corner of the rectangle.) The only case in which this won't work is when two of the points are in opposite corners of the rectangle and the third point "floats" inside it. In that case, you need to construct a smaller rectangle to create the last two right triangles (and also substract the area of the smaller rectangle, of course).

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