A solid has at its base the region bounded by the parabola x-y^2 = -8 and the left branch of the hyperbola x^2-y^2-4=0. The vertical slices perpendicular to the x-axis are squares. Find the volume of the solid. This is the full problem.

I was able to find out the points of intersection, which were x=-3 and x=4. I am not sure what the cross-sectional area is.