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Math Help - Area of rectangle with embedded parallelograms

  1. #1
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    Area of rectangle with embedded parallelograms

    Hello - I am new to the forum, and am at a loss at how to solve this problem. I need to find the area of the shaded region. I created a picture in paint. Can I get some help with this, and an explanation on how to solve this?

    Thank youQ\!
    Attached Thumbnails Attached Thumbnails Area of rectangle with embedded parallelograms-solve.jpg  
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  2. #2
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    Hello, ncooks!

    Welcome aboard!


    Find the area of the shaded region.
    Code:
                  9
          * - - - - - - - *
          |:::::::::::::::*
          |:::::::::::*   | 2
          |:::::::*     ..*
          |:::*       *:::*
          *       *:::::::|
          |   *:::::::::::*
       13 *::::::::::*    | 2
          |:::::::*     ..|
          |:::*       *:::*
          *       *:::::::|
          |   *:::::::::::|
          *:::::::::::::::|
          |:::::::::::::::|
          * - - - - - - - *

    The area of the rectangle is: .  9 \times 13 \:=\:117\text{ cm}^2


    Assuming that the diagonal lines are parallel,
    . . the white regions are two congeuent parallelograms,
    . . each with base 2 and height 9.

    The white region has area: . 2 \times (2\times 9) \:=\:36\text{ cm}^2


    Therefore, the area of the shaded region is: . 117 - 36 \:=\:81\text{ cm}^2


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~


    An easier way . . .

    Remove the white strips and push the shaded regions together.
    Code:
                  9
          * - - - - - - - *
          |:::::::::::::::*
          |:::::::::::*:::|
          |:::::::*:::::::|
        9 |:::*:::::::::::*
          *:::::::::::*:::|
          |:::::::*:::::::|
          |:::*:::::::::::|
          * - - - - - - - *
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