Area rule states that bodies with the same crossectional area distribution have the same drag. Does that mean I could use a straight wing on mach 1.2 aircraft with performance as high as sweep winged plane as long as they have the same area distribution?
A little more on the F104 vs sweept wings. In order to optimize a design for a given mach number greater than 1.0, the wing needs to be entirely enveloped within the mach pressure wave cone. Hence, large area with sweep or small area short and straight. Conversely, a long straight wing would be partially inside the mach cone and partially outside (not optimum).
Wing sweep is not required on supersonic aircraft. The F104 was a mach 2 interceptor with a straight, but tapered wing. It wasn't a well respected aircraft.
The Lockheed tests, however, determined that the most efficient shape for high-speed supersonic flight was a very small, straight, mid-mounted, trapezoidal wing.
You will generally want to have a Swept Wing for supersonic aircraft as the swept wing delays the formation of shock waves. The type of drag that a swept wing prevents is Wave Drag and would be a major source of drag at supersonic speeds. I believe that the "Area rule" that you are quoting refers only to parasitic drag. You may want to read this Wikipedia article on swept wings to learn more about their benefit. The main downside of using swept wings is wing tip stall but that can usually be overcome with a Washout design.
Another example of a supersonic aircraft that did not have swept wings is the Bell X1, the first aircraft to achieve supersonic speeds (and survive the experience). Given that the aircraft was pushing the unknown, the fuselage was shaped like a .50 caliber bullet, an object known to go supersonic smoothly... trial and error was a factor in pre computer aircraft design.
Note, though, that like the F104, the X1's wings are fairly short and set back on the fuselage, so that they are inside the shock wave cone coming off of the nose at supersonic speeds. As the X1 could barely go beyond Mach 1, its wings weren't as narrow as the F104, whose top speed was Mach 2.