# From unit circle to regular octagon and back

Geometry Level 4

In a unit circle, square $$ABCD$$ is inscribed. A new square $$A'B'C'D'$$ is constructed when the square $$ABCD$$ is translated by a vector $$\vec{AB}$$. Finally, an equilateral $$\triangle XYZ$$ is drawn, so that rectangle $$AB'C'D$$ is inscribed in it and the following is fulfilled:

• Points $$B' \wedge C' \in XY$$, $$A \in XZ$$ and $$D \in YZ$$.

Calculate the area of regular octagon whose side length is equal to the distance between points $$O$$ and $$Z$$. Give answer to 2 decimal places.

The image below represents how everything should look like when the drawing is done. Click here to enlarge the image.

Basically: Calculate the green region

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