OK, lets start with what we know. First off, how many peaks did you expect? Were there supposed to be 3, or 4, or how many components in your sample? Can you find out what the last person's or the next person's run looked like, and see any similarity? Did someone else run the same sample, things like that. See what the instructors say they can help you with. As I was taught in my first analytical chemistry course, no one drops a sample on your desk and says, "You the chemist, you figure out what it is." We generally know at least a little bit about what we're looking for. Run that by the instructors and see what they say.
I've only run a GC once, for the above mentioned Analytical Chemistry class. At that time, the GC's integrator failed, for reasons the T.A. couldn't explain, or fix in a reasonable time frame. So I just took the plots, and was told to use height to determine relative concentrations between standards and unknowns. Many people will react with a knee-jerk response against height quantification, but it can be necessary for bad peaks shapes, or adequate for some purposes. Again you have to see what the instructor says.
Now, the triangle method of determining peak over-lap is a method of determining the overlap area between two already integrated peaks. If you need to know the complete area under these poorly separated peaks, and the badly fronting final peak, a triangle isn't going to integrate it for you. An old trick that was related, but not taught, to me was: making copies of the curve, and carefully cut out the curves. Assuming paper is homogeneous (I suppose it is close enough,) and you wear gloves to avoid adding finger oils to the paper, and you've drawn and cut carefully, the mass of the cut out curves of paper can be used to find relative area. Again, the instructor will let you know if they like the idea or not.