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Math Help - Areas of triangles

  1. #1
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    Areas of triangles

    In \triangleABC, E and F are such that A-F-B and A-E-C. Segments BE and CF intersect at P. Area of \trianglePEC=4 and area of \trianglePFB=8 and area of \trianglePBC=10. Find the area of quadrilateral AFPE.
    I tried using reallyyyy many many approaches, even basic-most properties, but i couldn't get to it.
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  2. #2
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    Quote Originally Posted by amey View Post
    In \triangleABC, E and F are such that A-F-B and A-E-C. Segments BE and CF intersect at P. Area of \trianglePEC=4 and area of \trianglePFB=8 and area of \trianglePBC=10. Find the area of quadrilateral AFPE.
    I tried using reallyyyy many many approaches, even basic-most properties, but i couldn't get to it.
    I'm not sure that I understand your question correctly ...(?)

    If F is the midpoint of AB and if E is the midpoint of AC

    then the area of triangle BCE is as large as the area of triangle ABE.

    Therefore
     \Delta(BCE) = \Delta(ABE)

    (10+4) = 8+area(AFPE)

    Solve for area(AFPE)
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    Last edited by earboth; February 12th 2011 at 07:37 AM.
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  3. #3
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    Sorry, but A-F-B means points A, F and B are collinear. F is not midpoint of AB
    Last edited by amey; February 12th 2011 at 10:12 PM.
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  4. #4
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    Quote Originally Posted by amey View Post
    Sorry, but A-F-E means points A, F and E are collinear. F is not midpoint of AB
    Have you omitted some other bit of information?
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  5. #5
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    No. Atleast the problem is that way only.
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  6. #6
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    Easy solution, once one realises this is a mini "crossing ladder" classic problem; go here:
    Crossed Ladder Puzzle, Triangle Area Puzzle
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  7. #7
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    Thanks. I have got it now.
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