Shade region bounded by curves

Somewhere in the WWW the question was asked how to shade the region bounded by the following curves, where [math]\displaystyle{ x\ge 0 }[/math]:

[math]\displaystyle{ \begin{eqnarray*} x & \mapsto & \sqrt{x^2-1} \\ x & \mapsto & 0.707 x \\ x & \mapsto & 0 \\ \end{eqnarray*} }[/math]

Here it is:

0,0

–o+←↓↑→