It sounds like you have four equations of lines which somehow intersect to form a rectangle (or some quadrilateral if you are confusing terms). What you would do to find its area is to take the double integral over the edges of the quadrilateral, taking care to ensure you have the correct boundaries and proper integration order. Without more context though, your qeustion cannot be answered.
I assume you are looking for the corners of the rectangle.
This should work, if you are solving the right pairs of equations. If you post your attempt and the exact question we may be able to help you further.i already tried solving its intersection but it doesnt work out well...
If you haven't seen double integrals before, you can also do this by finding the lengths of 2 adjacent sides (after you have the corners) using the normal formula and multiply them together.