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Area of a Triangle

  1. May 26, 2008 #1
    1. The problem statement, all variables and given/known data

    The three vectors A, B, C point from the origin O to the three corners of a triangle. Show that the area of a triangle = 1/2 |( BxC + CxA + AxB )|

    2. Relevant equations

    1/2 |a x b| = 1/2 |a||b|sin(alpha)

    3. The attempt at a solution

    My initial attempt at this problem was to take the cross product like (Bx, By, Bz) x (Cx, Cy, Cz) and seeing if anything canceled. Unfortunately nothing did (I also tried with a '2d' vector (Bx, By, 0) etc and nothing canceled either).

    I believe I have to somehow use the equation I listed, but I'm not really sure what to do. It seems a little counterproductive to do the cross product three times. There aren't any simplifications that I can see. Anyone know where I should start?
  2. jcsd
  3. May 26, 2008 #2


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    For a triangle of side |a| and |b| with included angle [itex], what does [itex]\frac{1}{2} |a||b|sin\alpha[/itex] give?
  4. May 26, 2008 #3


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    Hi jesuslovesu! :smile:

    Hint: what is the area of triangle OAB? :smile:
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