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Math Help - Area of a Trapazoid...

  1. #1
    Junior Member
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    Thumbs down Area of a Trapazoid...

    Please look at the attached. The problem number I have to do is number 20. I believe the answer is 222. I

    Here is my math: 15/2 times 20 = 150

    12/2 times 12 = 72

    150 + 72 = 222

    Yes?
    Attached Thumbnails Attached Thumbnails Area of a Trapazoid...-math.jpg  
    Last edited by zachcumer; March 31st 2008 at 06:10 PM.
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  2. #2
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    Hello, zachcumer!

    Code:
        D *  *  *  *  *  *  * C
          *              *   *
          *           *       *
       12 *        * 20        * 15
          *     *               *
          *  *                   *
        A *   *   *   *   *   *   * B
    Area of a trapezoid: . A \;=\;\frac{h}{2}(b_1 + b_2)

    We know that: h = AD = 12
    . . But what are b_1 = CD\text{ and }b_2 = AB ?


    In right triangle CDA\!:\;\;CD^2 + AD^2 \:=\:AC^2\quad\Rightarrow\quad CD^2 + 12^2 \:=\:20^2
    . . CD^2 \:=\:256\quad\Rightarrow\quad \boxed{CD = 16}

    In right triangle ACB\!:\;\;AB^2 \:=\:AC^2 + BC^2\quad\Rightarrow\quad AB^2 \:=\:20^2 + 15^2
    . . AB^2 \:=\:625\quad\Rightarrow\quad \boxed{AB \:=\:25}


    Therefore: . A \;=\;\frac{12}{2}(16 + 25) \;=\;246

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