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Math Help - area of qudirilateral

  1. #1
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    area of qudirilateral

    In triangle ABC, E is a point on AC and F is a point on AB. The lines BE and CF intersect at D. If the areas of triangles BDF, BCD nad CDE are 3,7 and 7 respectively, what is the area of the quadrilateral AEDF
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  2. #2
    MHF Contributor red_dog's Avatar
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    area(BDC)=area(CDE)\Rightarrow BD=DE\Rightarrow area(ABD)=area(ADE)

    Let area(ADE)=x, \ area(ADF)=y. Then, x=y+3

    \frac{area(BDF)}{area(BDC)}=\frac{FD}{DC}=\frac{3}  {7}=\frac{area(AFD)}{area(ADC)}

    Then \frac{y}{x+7}=\frac{3}{7}\Rightarrow 7y=3x+21

    Solving the system \left\{\begin{array}{ll}x=y+3\\7y=3x+21\end{array}  \right. we get x=\frac{21}{2}, \ y=\frac{15}{2}

    area(AEDF)=x+y=18
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