# octagon shaded ara help

• December 2nd 2013, 05:59 PM
vegasgunner
octagon shaded ara help
http://data.artofproblemsolving.com/...d97dde279a.png

are there 4 right triangles that are not shaded, I am confused please help
• December 2nd 2013, 06:07 PM
LimpSpider
Re: octagon shaded ara help
OP, you really have to show some working!!!
• December 2nd 2013, 07:13 PM
vegasgunner
Re: octagon shaded ara help
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
• December 2nd 2013, 10:40 PM
Prove It
Re: octagon shaded ara help
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?
• December 3rd 2013, 07:20 AM
Soroban
Re: octagon shaded ara help
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 $ADEH$ minus the two right triangles.

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

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

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: $AD \:=\:2 + 2x$

You should be able to determine $x.$

Got it?