Why the obsession with triangles?
If you just want areas, or to know if a point is inside or outside the shape there is a better way.
Given a simple closed curve, points (ax, ay) (bx, by) (cx, cy) (dx, dy) as a trivial example.
Line them up a,b,c,d,a vertically and take the "determinant" as we were taught.
Axby - aybx + bxcy - bycx etc etc.
Divide the result by -2 and you have the are, positive is clockwise, negative is anticlockwise.
Put an anticlockwise shape inside a clockwise shape and you have a donut.
There is more, have to go to dinner.
If you just want areas, or to know if a point is inside or outside the shape there is a better way.
Given a simple closed curve, points (ax, ay) (bx, by) (cx, cy) (dx, dy) as a trivial example.
Line them up a,b,c,d,a vertically and take the "determinant" as we were taught.
Axby - aybx + bxcy - bycx etc etc.
Divide the result by -2 and you have the are, positive is clockwise, negative is anticlockwise.
Put an anticlockwise shape inside a clockwise shape and you have a donut.
There is more, have to go to dinner.