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Math Help - Trapezoid Area Formula

  1. #1
    Newbie Ai Ekio's Avatar
    Joined
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    Question Trapezoid Area Formula

    Usually I can figure out problems I'm having trouble with but I just can't figure this one out.
    It goes as follows:

    1.Draw a trapezoid.Label it's bases and height b1, b2, and h,respectively. Then draw a diagonal of the trapezoid.

    a.Write an expression for the area of each of the two triangles.

    b.Explain how you can justify the trapezoid area formula using the areas of the two triangles.


    Please explain it to me.Thank you.
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  2. #2
    Super Member

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    Hello, Ai Ekio!

    1. Draw a trapezoid.
    Label its bases and height b_1,\:b_2,\:h, respectively.
    Then draw a diagonal of the trapezoid.

    (a) Write an expression for the area of each of the two triangles.

    (b) Explain how you can justify the trapezoid area formula
    using the areas of the two triangles.
    Code:
                     b2
              B * * * * * * C 
               *:  *         *
              * :     *       *
             *  :h       *     *
            *   :           *   *
           *    :              * *
        A *  *  *  *  *  *  *  *  * D
                     b1

    (a) \Delta ABD has base b_1 and height h.
    . . . Its area is: . \frac{1}{2}b_1h

    . . \Delta BCD has base b_2 and height h.
    . . . Its area is: . \frac{1}{2}b_2h


    (b) The area of the trapezoid is the sum of the areas of the two triangles.

    . . A \;=\;\frac{1}{2}b_1h + \frac{1}{2}b_2h \quad\Rightarrow\quad A \;=\;\frac{1}{2}h(b_1+b_2)

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