• Dec 2nd 2013, 05:59 PM
vegasgunner
http://data.artofproblemsolving.com/...d97dde279a.png

• Dec 2nd 2013, 06:07 PM
LimpSpider
OP, you really have to show some working!!!
• Dec 2nd 2013, 07:13 PM
vegasgunner
Quote:

Originally Posted by LimpSpider
OP, you really have to show some working!!!

thanks for the help and your English is incorrect the correct term is you really have to show some work
• Dec 2nd 2013, 10:40 PM
Prove It
Quote:

Originally Posted by vegasgunner
thanks for the help and your English is incorrect the correct term is you really have to show some work

LimpSpider's English is fine. "Working" (or rather, "Working Out") can be a noun as well as a verb. And the OP is entirely correct. Just how many questions are you expecting us to do from your homework which you have not even attempted yourself?
• Dec 3rd 2013, 07:20 AM
Soroban
Hello, vegasgunner!

Quote:

Four diagonals of a regular octagon with the length of 2
intersect as shown. .Find the area of the shaded region.
Code:

```            B    2    C               o * * * o         2  *  *      *  2           *      *      *         *          *      *     A o * * * * * * * * * * * o D       * *:::::::::::::::*    *     2 *  *:::::::::::::::*  * 2       *    *:::::::::::::::* *     H o * * * * * * * * * * * o E         *      *          *           *      *      *             *      *  *               o * * * o             G        F```
Are there 4 right triangles that are not shaded? , Yes!

The shaded region is the rectangle \$\displaystyle ADEH\$ minus the two right triangles.

The right triangles have legs of length 2.
You can find their total area.

The rectangle has base \$\displaystyle AD\$ and height \$\displaystyle AH = 2.\$

We can find the length of the base with this diagram.

Code:

```                B      2      C                   o * * * * * o                 * :          : *           2  *  :          :  *  2             *    :x          :x    *           *      :          :      *         * 45o    :          :      45o*     A o  *  *  *  *  *  *  *  *  *  *  *  o D             x          2          x```
The base is: \$\displaystyle AD \:=\:2 + 2x\$

You should be able to determine \$\displaystyle x.\$

Got it?