you can replace x y instead of u v
i cant think of a way to find the are described here
I would start by drawing a picture with the boundary conditions: v = 0, v = 1, v = 2, |u| = 1, |u| = 2. These are all straight lines that will partition the plane into a number of rectangles. Pick a point in each rectangle and check whether or not it lies in your set. If a single point of the rectangle lies in your set, the entire rectangle (minus its boundary maybe) does! Conversely, if that point does not lie in the set, the entire rectangle will not (again, the boundary may be an exception).
You can check all rectangles like that. In the end you should have a pretty good picture of what your set looks like!
Separate names with a comma.