Thread: 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\!

Hello, ncooks!

Welcome aboard!

Find the area of the shaded region.

Code:

              9
      * - - - - - - - *
      |:::::::::::::::*
      |:::::::::::*   | 2
      |:::::::*     ..*
      |:::*       *:::*
      *       *:::::::|
      |   *:::::::::::*
   13 *::::::::::*    | 2
      |:::::::*     ..|
      |:::*       *:::*
      *       *:::::::|
      |   *:::::::::::|
      *:::::::::::::::|
      |:::::::::::::::|
      * - - - - - - - *

The area of the rectangle is: .


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: .


Therefore, the area of the shaded region is: .


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


An easier way . . .

Remove the white strips and push the shaded regions together.

Code:

              9
      * - - - - - - - *
      |:::::::::::::::*
      |:::::::::::*:::|
      |:::::::*:::::::|
    9 |:::*:::::::::::*
      *:::::::::::*:::|
      |:::::::*:::::::|
      |:::*:::::::::::|
      * - - - - - - - *