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Find area using vectors (cross product)

  1. Sep 3, 2014 #1
    1. The problem statement, all variables and given/known data
    Hello, I've been trying to solve this problem, but in the examples that my teacher gave me didn't include something like this, I know how to calculate area but only if I have all the coordinates established.
    I need to find the area using the cross product.

    Untitled.jpg

    2. Relevant equations
    a92ba9287031332f696b2ae85382e1aa.png


    3. The attempt at a solution
    I know I must divide the polygon into triangles, so I can calculate the area.
    I need a starting point for the coordinates.
    For example I can call the starting point A.
    A(0,0)
    Then I need more coordinates in order to establish each vector.
    B(0,1.03)
    C(0,1.12)

    After that...
    AB = 0i + 1.03j
    AC = 0i + 1.12j
    CB = 0i + 2.15j

    A=[itex]\frac{1}{2}[/itex](AB x AC)

    If what I wrote above is right then I think I can solve It, but I'm almost absolutely sure that is wrong.
    I need to know how to declare each vector so I can calculate the area.
    I hope is clear enough, and thanks in advance for taking your time to read and help me with this problem.
     
  2. jcsd
  3. Sep 3, 2014 #2

    jedishrfu

    Staff: Mentor

    Do you know geometrically what area the cross product represents?

    Next you need the identify the points on the diagram.

    I assume you meant point A to be the one in the lower left
    and that the x axis is along the lower left boundary line, correct?

    If so then the vectors you've written are wrong:

    AB = <1.03, 0>

    And

    AC = <0, 1.14>

    ...
     
    Last edited: Sep 3, 2014
  4. Sep 3, 2014 #3

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    That isn't correct without absolute value signs. The area is numerically equal to 1/2 the length of the cross product.

    Offhand, I don't think your problem has a solution. I don't think knowing the lengths of the sides of a pentagon is enough information to determine its area. Is there more information you haven't included?
     
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