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Math Help - Solving for the area of a triangle in a quadrilateral

  1. #1
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    Solving for the area of a triangle in a quadrilateral

    Hi Guys,

    I've never been good with geometry, and this one just has me stumped. I cannot find any ratios to help me solve the problem.

    I will use [ ] to denote area.

    We have quadrilateral ABCD, and the point E which is the intersection of the diagonals of ABCD. [AEB] = 3, [DEC] = 10, [BEC] = 2 *[AED]
    Compute [AED].
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  2. #2
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    Re: Solving for the area of a triangle in a quadrilateral

    Hey ShadowKnight8702.

    In your quadrilateral you have [ABCD] = [AEB] + [DEC] + [BEC] + [AED] = [AEB] + [DEC] + 2*[AED] (using the definition that the whole quadrilateral is the sum of each of the quarters separated from the mid-point E and the appropriate lines.
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  3. #3
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    Re: Solving for the area of a triangle in a quadrilateral

    Hi,
    The answer is \sqrt{15}. The attachment shows how to arrive at this. I had fun constructing an accurate drawing of the situation.

    Solving for the area of a triangle in a quadrilateral-mhfgeometry36.png
    Thanks from ShadowKnight8702
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  4. #4
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    Re: Solving for the area of a triangle in a quadrilateral

    Thanks a bunch johng
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