How Do You Calculate the Area of a Quadrilateral Using Vertices?

[numb_dumb]

A(2,1) b(8,1) C(4,3) D(6,6)

let these be 4 points(vertices) of a quadrilateral

so i calculated it out as

2 1
8 1
4 3
6 6
2 1

multiplying diagonal elements
Area = |(2*1-8*1)+(8*3-1*4)+(4*6-3*6)+(6*1-2*6)/2|=7
but the answer is 14 and it gives different answers for different choice of co-ordinate order
so how to judge which one is correct?
any limitation to use this rule?
my heads going crazy over this...

 

[willem2]

You're trying to use the fact that the area of a convex quadrilateral is the absolute value of half the cross-product of the diagonals? It's easier to compute the diagonals first, and make sure that the lengths you compute are really those of the diagonals

If you draw a lines between adjacent points in the order you've given you don't get a convex polygon.