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Math Help - Area Of A Parellelogram

  1. #1
    Member Rimas's Avatar
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    Area Of A Parellelogram

    The Area Of A Parallelogram can be given in terms of the lengths x and y of two adjacent sides and a trigonometric function of the angle formed by those two sides. Which of the following formulas gives the area A of this parallelogram and why?

    A. A=xy cos(o)
    B. A=xy tan(o)
    C. A=xy sin(o)
    D. A=xy cot(o)
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Rimas View Post
    The Area Of A Parallelogram can be given in terms of the lengths x and y of two adjacent sides and a trigonometric function of the angle formed by those two sides. Which of the following formulas gives the area A of this parallelogram and why?

    A. A=xy cos(o)
    B. A=xy tan(o)
    C. A=xy sin(o)
    D. A=xy cot(o)
    the answer is C, A = xysin(0)

    Hint:

    for parallelogram,
    Area = base * height

    can you get it now?
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  3. #3
    Member Rimas's Avatar
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    Could you expand on that answer a little bit more because i thought sin = opposite over hypotenuse but there is no hypotenuse here.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Rimas View Post
    Could you expand on that answer a little bit more because i thought sin = opposite over hypotenuse but there is no hypotenuse here.
    actually, there is a hypotenuse. on the left side, x is the hypotenuse. maybe a modified diagram will help. can you do it after seeing the following?

    Note: the height i mentioned in my previous post is the vertical height
    Attached Thumbnails Attached Thumbnails Area Of A Parellelogram-parallelogram.gif  
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  5. #5
    Junior Member Godfather's Avatar
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    Quote Originally Posted by Jhevon View Post
    actually, there is a hypotenuse. on the left side, x is the hypotenuse. maybe a modified diagram will help. can you do it after seeing the following?

    Note: the height i mentioned in my previous post is the vertical height
    So the Sin of (O) = Z/X *(X)*(Y)
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Godfather View Post
    So the Sin of (O) = Z/X *(X)*(Y)
    um, no. sine = opp/hyp

    so sin(o) = z/x
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  7. #7
    Junior Member Godfather's Avatar
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    Quote Originally Posted by Jhevon View Post
    um, no. sine = opp/hyp

    so sin(o) = z/x
    So u get Z/X but what does that do for u
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Godfather View Post
    So u get Z/X but what does that do for u
    ok, here it is:

    see diagram below.

    let the vertical height be z.

    for a parallelogram, A = height*base

    remember, the height is z, but we have:

    sin(o) = z/x
    => z = xsin(0) ........this is the formula for the vertical height.

    the base is y

    so, A = height*base = y * xsin(0) = xysin(0)
    Attached Thumbnails Attached Thumbnails Area Of A Parellelogram-parallelogram.gif  
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