http://data.artofproblemsolving.com/...d97dde279a.png

are there 4 right triangles that are not shaded, I am confused please help

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- Dec 2nd 2013, 05:59 PMvegasgunneroctagon shaded ara help
http://data.artofproblemsolving.com/...d97dde279a.png

are there 4 right triangles that are not shaded, I am confused please help - Dec 2nd 2013, 06:07 PMLimpSpiderRe: octagon shaded ara help
OP, you really have to show some working!!!

- Dec 2nd 2013, 07:13 PMvegasgunnerRe: octagon shaded ara help
- Dec 2nd 2013, 10:40 PMProve ItRe: octagon shaded ara help
- Dec 3rd 2013, 07:20 AMSorobanRe: 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

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 *

* : : *

* 45^{o}: : 45^{o}*

A o * * * * * * * * * * * o D

x 2 x

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

Got it?