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Homework Help: Area of Triangle in 3D

  1. Aug 22, 2010 #1
    1. The problem statement, all variables and given/known data
    The vertices of triangle are (2,0,0) ; (0,3,0) ; (0,0,6) . Find the area of triangle.


    2. Relevant equations



    3. The attempt at a solution
    is it right that i put in determinant like
    Area of triangle =
    0.5 | 2 0 0 |
    | 0 3 0 |
    | 0 0 6 |
    = 0.5 (2* 3 * 6)
    = 18 .

    but i think this method is wrong ... the answer of this question is 3 sqrt ( 14) .
     
  2. jcsd
  3. Aug 22, 2010 #2
    In your approach what you are doing is not the area of a triangle.

    You are actually finding the volume of a parallelepiped.

    The area of the triangle will always be [tex] A= \frac{1}{2} *base*height[/tex]


    You have points so you can find the lengths of the base and height.

    A quick sketch may be needed.
     
  4. Aug 22, 2010 #3

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    It's also half the length of the cross product of two difference vectors along the edges of the triangle. You can use a determinant type form to work out the cross product.
     
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