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Math Help - Equal Areas of triangles and quadrilateral

  1. #1
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    Equal Areas of triangles and quadrilateral

    Hello,

    please help,

    Given an arbitrary convex quadrilateral ABCD.
    K is the center point of line segment AB.
    M is the center point of line segment CD.
    AM \cap KD=N, BM \cap KC=L.
    Prove that: Area(KLMN)=Area(\triangle AND) + Area (\triangle BCL).

    In attachment is picture.

    Equal Areas of triangles and quadrilateral-cetvorougao.gif

    Thank you!
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  2. #2
    MHF Contributor
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    Hint: Using the fact that the altitude from K to DC is the arithmetic mean of the altitudes from A and B, prove that the \mathop{\mathrm{Area}}(\triangle ADM)+\mathop{\mathrm{Area}}(\triangle BMC)=\mathop{\mathrm{Area}}(\triangle KDC).
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