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Area of triangle inside parallelogram

  1. Jan 23, 2010 #1
    1. The problem statement, all variables and given/known data

    http://folk.uio.no/robinbj/gg/ggstart.pdf" [Broken]
    I am supposed to find the area of the triangle PQD. The numbers given are the areas of the other triangles.


    2. Relevant equations
    [tex]A= \frac{1}{2} a b \sin{C}[/tex]

    As well as Heron's formula, possibly?
    [tex]A= \sqrt{s(s-a)(s-b)(s-c)}[/tex] where [tex]s = \frac{a+b+c}{2}[/tex]

    3. The attempt at a solution
    Where I'm stumped is exactly how to start. At first, I figured I'd try to find the values of a, b and c. Using the area of a triangle:

    [tex]a = DP = \frac{14}{AP\sin{\theta}}[/tex]

    Similarly, for b:

    [tex]b = QP = \frac{56}{QB\sin{\alpha}}[/tex]

    And c:

    [tex] c = QD = \frac{28}{QC\sin{x}} [/tex]

    Meaning that [tex]s = \frac{7}{AP\sin{\theta}} + \frac{28}{QB\sin{\alpha}} + \frac{14}{QC\sin{x}} [/tex]

    However, dealing with three different angles, without knowing the relationship between them or the sum of the angles, I just don't know how to proceed and solve the exercise based on this. I am not looking for a solution from you guys, mind you. Just a tip to get me on the right track?

    Thank you.
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Jan 23, 2010 #2

    tiny-tim

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    Homework Helper

    Hi cjwalle! :smile:

    I don't think the angles matter …

    won't the ratios be the same, whatever the angles are, so you might as well make it a square?
     
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