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]x\ge 0[/math]:

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