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Math Help - Find Area of Quadrilateral

  1. #1
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    Find Area of Quadrilateral

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

    Since I do not know which quadrilateral it is, I decided to graph the points given on the xy-plane.

    I determined it is a parallelogram or so I think.

    I found the base to be 11 and height to be 8.

    So, A = bh, which is A = 11*8 or 88 but I am wrong according to the math book.

    Who is right and why?

    Thank you
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  2. #2
    Super Member Matt Westwood's Avatar
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    Here's an idea.

    Split it up into 4 triangles and a rectangle and add them all up together, like this:

    First triangle: (-4, -2), (0, -2), (0, 5)

    2nd tri: (0, 5), (0, 3), (9, 3)

    3rd tri: (9, 3), (7, 3), (7, -3)

    4th tri: (7, -4), (7, -2), (-4, -2)

    Then the rectangle in the middle is (0, -2), (0, 3), (7, 3), (7, -2).

    Drawing a picture again should help. It should be easy to calculate this.

    Note that you have 2 pairs of triangles which are the same size, which should make the calculation even easier.
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  3. #3
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    But...

    Quote Originally Posted by Matt Westwood View Post
    Here's an idea.

    Split it up into 4 triangles and a rectangle and add them all up together, like this:

    First triangle: (-4, -2), (0, -2), (0, 5)

    2nd tri: (0, 5), (0, 3), (9, 3)

    3rd tri: (9, 3), (7, 3), (7, -3)

    4th tri: (7, -4), (7, -2), (-4, -2)

    Then the rectangle in the middle is (0, -2), (0, 3), (7, 3), (7, -2).

    Drawing a picture again should help. It should be easy to calculate this.

    Note that you have 2 pairs of triangles which are the same size, which should make the calculation even easier.
    It is easy now but how did you determine those extra points?
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  4. #4
    Super Member Matt Westwood's Avatar
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    I drew it. Draw it yourself and it should be easy to work out how to do it.
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  5. #5
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    ok...

    Quote Originally Posted by Matt Westwood View Post
    I drew it. Draw it yourself and it should be easy to work out how to do it.
    It's a rectangle not a parallelogram. I will use graphing paper next time.
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