Area of a surface inside a cylinder

**Find the area of that part of the surface z = xy inside the cylinder x^2 +y^2 = a^2.**

Well I don't know what the surface looks like but I have an idea of what the cylinder looks like.

It's like drawing a circle in the xy plane centered at the origin with radius a and pulling that circle in the z direction to create a cylinder.

Again, I don't know what surface looks like but the area of the surface should be

$\displaystyle \int\int_{S_{xy}} \sqrt{1 + (\frac{\partial z}{\partial x})^{2} + (\frac{\partial z}{\partial y}})^{2}}dA.$

If I take the partials accordingly and plug them in I get

$\displaystyle \int \int_{S_{xy}} \sqrt{1 + x^{2} + y^{2}}}dA$

now I'm stuck.

Any ideas?