Comment by gloftus

Worth noting that the hyperbolic triangle in the article contains "points at infinity" which are not actually a part of the hyperbolic plane, so this is really an "improper triangle" as the article notes. One could construct a similar improper triangle in the Euclidean plane that consisted of two parallel lines meeting at infinity. Such a triangle would still have 180 degrees of internal angle but it's area and perimeter would be infinite.