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Math Help - Area of Isosceles Trapezoid

  1. #1
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    Area of Isosceles Trapezoid

    Hi there,

    How do you find the area of an Isosceles trapezoid if all you have is that the altitude is 15 inches and the diagonal is 25 inches?
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  2. #2
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    Aaaaay, The Fonz!

    Find the area of an Isosceles trapezoid with altitude 15 and diagonal 25.
    Code:
                  A       x       B
                  *---------------*
                 /:  *            :\
                / :     *         : \
               /  :        *      :  \
              /   :        25 *   :   \
             /  15:              *:    \
            /     :               : *   \
           /      :               :    * \
        D *-------*---------------*-------* C
          : 20-x  E       x       F 20-x  :
                  : - - - -  20 - - - - - :

    We have isosceles trapezoid ABCD with diagonal AC = 25
    . . and altitudes AE = BF = 15.


    In right triangle AEC\!:\;\;AE^2 + EC^2 \:=\:AC^2 \quad\Rightarrow\quad 15^2 + EC^2 \:=\:25^2

    . . Hence: . EC^2 \:=\:400 \quad\Rightarrow\quad EC \:=\:20


    Let AB \,=\,EF \,=\,x
    . . Then: . FC\,=\,DE \,=\,20-x

    Hence: . DC \:=\:(20-x) + x + (20-x) \:=\:40-x


    The area of a trapezoid is: . A \;=\;\frac{h}{2}(b_1 + b_2)

    We have: . A \;=\;\frac{AE}{2}(AB + DC) \;=\;\frac{15}{2}\bigg[x + (40-x)\bigg] \;=\;\frac{15}{2}\cdot40 \;=\;\boxed{300}

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