are there 4 right triangles that are not shaded, I am confused please help
Hello, vegasgunner!
Four diagonals of a regular octagon with the length of 2
intersect as shown. .Find the area of the shaded region.
Are there 4 right triangles that are not shaded? , Yes!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.
The base is: $\displaystyle AD \:=\:2 + 2x$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?