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Area of a Quadrilateral

  1. Oct 24, 2011 #1
    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....
  2. jcsd
  3. Oct 24, 2011 #2
    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.
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