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Math Help - parallelogram area help

  1. #1
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    parallelogram area help

    Find the area of the parallelogram with vertices at (1,4), (2,-5), (5,-2) and (4,7)

    I know the formula is ad-bc


    however how do i work out what the vectors (a,b) and (c,d) are?


    its suppose to be (3,3) and (1,-9)

    I have drawn a diagram, but it still does not help, what are the non-parallel edges?
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  2. #2
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    Re: parallelogram area help

    Hey Tweety.

    Did you plot the figure geometrically? Also remember to break things up into triangles and add the areas.

    Hint: The length of the vector |axb| gives the area of the triangle that is enclosed within the vectors a and b.
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  3. #3
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    Re: parallelogram area help

    No, chiro. |a x b| gives the area of the parallelogram having vectors a and b as two sides. The area of the triangle is (1/2)|a x b|.
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  4. #4
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    Re: parallelogram area help

    Yes you are spot on: thanks for picking that up! (1/2absin(C) = 1/2 |axb|).
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  5. #5
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    Re: parallelogram area help

    Quote Originally Posted by Tweety View Post
    Find the area of the parallelogram with vertices at (1,4), (2,-5), (5,-2) and (4,7)
    I know the formula is ad-bc
    however how do i work out what the vectors (a,b) and (c,d) are?
    its suppose to be (3,3) and (1,-9)
    I have drawn a diagram, but it still does not help, what are the non-parallel edges?
    @Tweety, I am constantly amazed how little you seem to know about questions that you are asked to solve.
    If you have not been taught this theorem then your course is a SHAM

    Theorem: If \vec{A}~\&~\vec{B} are adjacent sides of a parallelogram then
    \|\vec{A}\times\vec{B}\| is the area of that parallelogram.
    Thanks from Tweety
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  6. #6
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    Re: parallelogram area help

    errmm well I know this formula, but my problem was I did not know 'how to apply it, and also I missed classes when this was being taught so i am just reading it off a text book......
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  7. #7
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    Re: parallelogram area help

    To find the coordinates of a vector, subtract the coordinates of the beginning from those of the end.

    This follows from the definition of coordinates and operations of vectors. In my course, the coordinates of a point are by definition the coordinates of the radius-vector to that point. That is, if O is the origin, the coordinates of a point A are the coordinates of the vector OA. Now, a vector AB equals OB - OA, so the coordinates of AB are the coordinates of B minus the coordinates of A.
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