# Thread: Area of rectangle with embedded parallelograms

1. ## 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\!

2. Hello, ncooks!

Welcome aboard!

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

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

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: .$\displaystyle 2 \times (2\times 9) \:=\:36\text{ cm}^2$

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

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

An easier way . . .

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