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, 06:59 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, 07:07 PMLimpSpiderRe: octagon shaded ara help
OP, you really have to show some working!!!

- Dec 2nd 2013, 08:13 PMvegasgunnerRe: octagon shaded ara help
- Dec 2nd 2013, 11:40 PMProve ItRe: octagon shaded ara help
- Dec 3rd 2013, 08:20 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 minus the two right triangles.

The right triangles have legs of length 2.

You can find their total area.

The rectangle has base and height

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

Got it?