Area of rectangle with embedded parallelograms

Hello, ncooks!

Welcome aboard!

Quote:

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: . $117 - 36 \:=\:81\text{ cm}^2$

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An easier way . . .

Remove the white strips and push the shaded regions together.

Code:

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