Original Post
This topic is somewhat old I'm sure: Computing the area of a triangle in planar space (2 dimensional) is simple: for a triangle (x1,y1) - (x2, y2) - (x3, y3) V = 1/2((x2 - x1)(y3 - y1) - (x3 - x1)(y2 - y1)) //It is half the perp dot product of two edges The best I've come up with for 3 dimensional is this: //First get vectors for two edges of the triangle U.x=x2-x1: U.y=y2-y1: U.z=z2-z1 V.x=x3-x1: V.y=y3-y1: V.z=z3-z1 D.x = U.y*V.z-V.y*U.z: D.y = V.x*U.z-U.x*V.z: D.z = U.x*V.y-V.x*U.y Area = sqrt(D.x^2 + D.y^2 + D.z^2)/2; in notation A=|UxV|/2 Essentialy this is half the magnitude of the cross product of the two vectors. So my wonder is, why should we need to use a square root operation to obtain the area of a triangle in 3D.
