Question

can someone explain how the formula in this link come from?
I used to use this formula, but never know, where is it come from :D
http://www.mathopenref.com/coordpolygonarea.html

thanks

Answer 1

it's simple. the area of the triangle whose vertices (in counterclockwise order) (x1,y1), (x2,y2) and (x3,y3) is given by the determinant \[\frac{ 1 }{ 2 }\left[\begin{matrix}x1 & y1 & 1 \\ x2 & y2 & 1\\x3 & y3 & 1\end{matrix}\right]\]

Answer 2

now break the quadrilateral into two triangles, and apply the formula abobe.

Answer 3

@chihiroasleaf if the order of the points is counterclockwise, the value of the deteminant is negative.