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Math Help - Area - Problem Sum

  1. #1
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    Area - Problem Sum

    A Villager David has a plot of land of the shape of a quadrilateral. The Village head decided to take over some portion of his plot from one of the corners toconstruct a health center. Suzie Agrees to the above proposal with the condition that he should be given equal amount of land in lieu of his land adjoining his plot so as to form a triangular plot. Explain how this plan can be implemented.

    Please solve this
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  2. #2
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    Quote Originally Posted by shaurya View Post
    A Villager David has a plot of land of the shape of a quadrilateral. The Village head decided to take over some portion of his plot from one of the corners toconstruct a health center. Suzie Agrees to the above proposal with the condition that he should be given equal amount of land in lieu of his land adjoining his plot so as to form a triangular plot. Explain how this plan can be implemented.

    Please solve this
    Hi,

    I've attached a sketch of the transformation.

    The rectangle is painted in red, the triangles are painted in blue.
    Attached Thumbnails Attached Thumbnails Area - Problem Sum-rect_to_triangl.gif  
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  3. #3
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    Earboth: It's in the shape of a quadrilateral, not a pentagon.

    Hint: Try forming a square and splitting it up into four congruent triangles.
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  4. #4
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    Can anyone post it using theorums

    between the same base and equal parralles.
    It would be much easier like that. Earthbot if you can help me.

    @ SnipedYou : We cant assume that its a square or a parrallelogram. We just know its a quadrilateral. may it be a trapeizum or watsoever.
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  5. #5
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    Quote Originally Posted by shaurya View Post
    Can anyone post it using theorums

    between the same base and equal parralles.
    It would be much easier like that. Earthbot if you can help me.

    ...
    Hi,

    I'll try. I've attached a sketch of a quadrilateral ABCD.

    1. Draw the diagonal DB
    2. Draw a parallel of DB through C
    3. This parallel intersect with AB in E
    4. The area \ of\  \Delta DBC = area \ of \ \Delta DBE (same base, same height)
    5. The area a(\Delta DFC) = a(\Delta BFE)
    6. Cut off \Delta DFC and glue to the rest the \Delta FBE
    Attached Thumbnails Attached Thumbnails Area - Problem Sum-viereck_zu_dreieck.jpg  
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