The figure shows the surface created when the $\displaystyle cylinder\ y^2 + z^2 = 1\ intersects\ the\ cylinder\ x^2 + z^2 = 1\ Find\ the\ area\ of\ this\ surface.$

I think to find the surface integral we need to do the double integral of ru cross rv, with respect to du and dv respectively. However, im not even sure how to get to that point.