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Math Help - Area Of Trapezium

  1. #1
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    Question Area Of Trapezium

    The perimeter of a trapezium is 104 m; its non-parallel sides are 18 m & 22 m & its altitude is 16 m. How do I find the area of the trapezium?

    Thanks,

    Ron
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    Quote Originally Posted by rn5a View Post
    The perimeter of a trapezium is 104 m; its non-parallel sides are 18 m & 22 m & its altitude is 16 m. How do I find the area of the trapezium?

    Thanks,

    Ron
    I don't really know if it will help.

    Find the mid-segment and multiply him by the height(16m).
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  3. #3
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    The Area is the height times the average of the bases. The sum of the bases is 104-18-22. Can you take it from here?
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  4. #4
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    Quote Originally Posted by DrSteve View Post
    The Area is the height times the average of the bases. The sum of the bases is 104-18-22. Can you take it from here?
    I tried what you suggested but can't proceed ahead. How do I get the average of the bases from the sum of the bases? Can you please help me out? Thanks

    OK.....I got it.........thanks a lot.......
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  5. #5
    MHF Contributor Also sprach Zarathustra's Avatar
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    Quote Originally Posted by rn5a View Post
    I tried what you suggested but can't proceed ahead. How do I get the average of the bases from the sum of the bases? Can you please help me out? Thanks

    OK.....I got it.........thanks a lot.......
    S is the area.

    We have this formula for an area of trapezium:

    S=m\cdot h

    Where h is the height and m is mid-segment of trapezium, or:

    m=\frac{a+b}{2}

    Lets find first a+b.

    a+b=104-18-22=64

    Therefor \frac{a+b}{2}=\frac{64}{2}=32

    S=m\cdot h=32\cdot 16=2^5 \cdot 2^4=2^9=512
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  6. #6
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    Hello, Ron!

    The perimeter of a trapezium is 104 m.
    Its non-parallel sides are 18 m & 22 m.
    Its altitude is 16 m.
    How do I find the area of the trapezium?
    Use the area formula.

    Formula: . \boxed{A \;=\;\tfrac{1}{2}h(b_1 + b_2)}

    . . where . \,h = height, b_1,b_2 = parallel sides.


    Code:
    
                      b1
                *  *  *  *  *
               *              *
           18 *                 *  22
             *                    *
            *                       *
           *                          *
          *  *  *  *  *  *  *  *  *  *  *
                         b2

    The perimeter is 104 m.

    . . b_1 + 22 + b_2 + 18 \:=\:104 \quad\Rightarrow\quad \boxed{b_1 + b_2 = 64}


    We are given: . \boxed{h \,=\,16}


    Substitute into the formula . . .

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