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Math Help - area of parallelograms and trapezoids

  1. #1
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    area of parallelograms and trapezoids

    If NS=16 find the area of parallelogram MNOP. This problem is really hard. I need to know how to do it with work. I also know that the answer is 122 but i need work to go with it. the problem can be solved using a proof or by using algebra. Yeah sorry i forgot to mention that MN=10, RS=8, ST= 3, and OV=9. This picture is not drawn to scale.
    Attached Thumbnails Attached Thumbnails area of parallelograms and trapezoids-geometry.bmp  
    Last edited by mizzell; February 9th 2010 at 08:21 AM.
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  2. #2
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    More information please

    Hello mizzell

    Welcome to Math Help Forum!
    Quote Originally Posted by mizzell View Post
    If NS=16 find the area of parallelogram MNOP. This problem is really hard. I need to know how to do it with work. I also know that the answer is 122 but i need work to go with it. the problem can be solved using a proof or by using algebra.
    There must be some details that you haven't told us - we don't have enough here to calculate the area. Please check the question again, and give us more information.

    Grandad
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  3. #3
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    Quote Originally Posted by mizzell View Post
    If NS=16 find the area of parallelogram MNOP. This problem is really hard. I need to know how to do it with work. I also know that the answer is 122 but i need work to go with it. the problem can be solved using a proof or by using algebra. MN=10, RS=8, ST= 3, and OV=9. This picture is not drawn to scale.
    The green parallelogram is the difference of the sum of two trapezoids.
    (See attachment)

    2 orange - 2 blue = 1 green
    Attached Thumbnails Attached Thumbnails area of parallelograms and trapezoids-trapez_differenz.png  
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  4. #4
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    Quote Originally Posted by mizzell View Post
    If NS=16 find the area of parallelogram MNOP. This problem is really hard. I need to know how to do it with work. I also know that the answer is 122 but i need work to go with it. the problem can be solved using a proof or by using algebra. Yeah sorry i forgot to mention that MN=10, RS=8, ST= 3, and OV=9. This picture is not drawn to scale.
    1. Compare the trapezoid RSNM with the trapezoid TVOP. You can show that VT = 8 and PT = 3.

    2. Have a look here: http://www.mathhelpforum.com/math-he...rapezoids.html
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    What do u mean by compare those two trapezoids and how did u VT and PT? Also that link you gave me does not work.
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  6. #6
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    Quote Originally Posted by mizzell View Post
    What do u mean by compare those two trapezoids and how did u VT and PT?
    Also that link you gave me does not work. <<<< it's post #3 (the mods transfered my reply to your double post into this thread)
    \overline{MN} \parallel \overline{PO}~\wedge~ |\overline{MN}| = |\overline{PO}|~\implies~|\overline{RS}| = |\overline{TV}|

    |\overline{SN}| - |\overline{RM}| = 6~\implies~|\overline{OV}| - |\overline{PT}| = 6

    Solve for |\overline{PT}|
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