Calculate the area of the cone $\displaystyle \ z = \sqrt {x^2 + y^2}$, that is inside cylinder $\displaystyle x^2 + y^2 \leq 2x$, outside the cylinder $\displaystyle x^2 + y^2 \leq 1$ and above the plane xy.

A.: $\displaystyle \frac {\sqrt{2} (2\pi + 3 \sqrt{3})} {6}$