Compute area of arbitrary tetrahedral in cartesian coordinates

Question

suppose that with given 4 vertexes in Cartesian plane we want to find the area of Quadrilateral in general . with four points : $(a_i,b_i)$ for $i=1,..,4$. what is the general formula with respect to vertexes? thanks

Answer 1

You can use the shoelace formula, that, witn your notation, becomes: $$ A=\frac{1}{2}|a_1b_2+a_2b_3+a_3b_4+a_4b_1-a_2b_1-a_3b_2-a_4b_3-a_1b_4| $$