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Formulae for calculating the area of a quadrilateral non-cyclic

  1. Jun 12, 2015 #1
    I want knows if a formula for calculate the area of a quadrilateral non-cyclic needs of just four values (the values of the four edges) or if is necesseray 6 values (the values of the four edges MORE os values of the two diagonals)?

    This formula needs of 6 values (a,b,c,d,p,q):
    1a04d408f073f30a1edd47b9f4501566.png

    OBS: s = (a+b+c+d)/2

    And this formula needs of just 4 (a,b,c,d):
    3227d258f1f0437e6cad6f6000c9c479.png

    But, I tested this second formula in the geogebra and it don't works...

    Sources:
    http://en.wikipedia.org/wiki/Trapezoid#Area
    http://en.wikipedia.org/wiki/Quadrilateral#Non-trigonometric_formulas
    https://en.wikipedia.org/wiki/Bretschneider's_formula#Related_formulas
     
  2. jcsd
  3. Jun 12, 2015 #2

    mathman

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    Science Advisor
    Gold Member

    The four edges are obviously not sufficient. Start with a square (side length=1) - area =1. Now take a pair of diagonally opposite corners and move them toward each other, while keeping the side lengths constant. When they meet, the resultant quadrilateral area = 0.
     
  4. Jun 13, 2015 #3
    And 4 sides and 1 diagonal is not sufficient either. Consider a shape with sides 1, 1, 0.8, 0.8 in that order. Now the 0.8 v can be inside, or outside (convex or concave) with the area different.
     
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