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Math Help - Find Area of Quadrilateral

  1. #1
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    Find Area of Quadrilateral

    Find the area of the quadrilateral whose vertices are
    A(-4,-2), B(0,5), C(9,3) and D(7,-4).

    I thought it was a trapezoid after plotting and connecting each point and thus my answer was area = 40 but I was wrong.
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  2. #2
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    [quote=magentarita;282648]Find the area of the quadrilateral whose vertices are
    A(-4,-2), B(0,5), C(9,3) and D(7,-4).

    I thought it was a trapezoid after plotting and connecting each point and thus my answer was area = 40 but I was wrong.[/quote


    ignore this
    Last edited by mathaddict; March 15th 2009 at 08:56 AM.
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  3. #3
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    Quote Originally Posted by magentarita View Post
    Find the area of the quadrilateral whose vertices are
    A(-4,-2), B(0,5), C(9,3) and D(7,-4).

    I thought it was a trapezoid after plotting and connecting each point and thus my answer was area = 40 but I was wrong.
    I've attached a sketch of the quadrilateral. By first inspection it looks like an irregular quadrilateral.

    Construct a rectangular "container" such that the quadrilateral is inscribed into this container. Calculate the area of the rectangle and subtract the areas of the 4 right triangles:

    a_{rectangle} = 9 \cdot 13 = 117
    a_1=\frac12 \cdot 2 \cdot 11 = 11
    a_2=\frac12 \cdot 2 \cdot 7 = 7
    a_3=\frac12 \cdot 2 \cdot 9 = 9
    a_4=\frac12 \cdot 4 \cdot 7 = 14

    Therefore \boxed{a_{ABCD} = 76}
    Attached Thumbnails Attached Thumbnails Find Area of Quadrilateral-area_iireg4gon.png  
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  4. #4
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    I see...

    Quote Originally Posted by earboth View Post
    I've attached a sketch of the quadrilateral. By first inspection it looks like an irregular quadrilateral.

    Construct a rectangular "container" such that the quadrilateral is inscribed into this container. Calculate the area of the rectangle and subtract the areas of the 4 right triangles:

    a_{rectangle} = 9 \cdot 13 = 117
    a_1=\frac12 \cdot 2 \cdot 11 = 11
    a_2=\frac12 \cdot 2 \cdot 7 = 7
    a_3=\frac12 \cdot 2 \cdot 9 = 9
    a_4=\frac12 \cdot 4 \cdot 7 = 14

    Therefore \boxed{a_{ABCD} = 76}
    I like your reply and explanation.
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