In fuzzy set theory, the distance and entropy measure of intuitionistic fuzzy sets (IFSs) have received extensive concern because of the capability for handling imprecise or uncertain problems. However, most of the existing modeling methods for distance and entropy measure are imperfect in teams of intelligibility and performance. In this work, we proposed a new geometric modeling method that can be simultaneously used for distance and fuzzy entropy modeling of IFSs. We used rigorously mathematical derivation to prove that the proposed distance and fuzzy entropy measures satisfy the properties of the definitions. In the experiments, we applied the proposed distance and fuzzy entropy measure into pattern recognition, medical diagnosis, and multi-attribute decision making to examine the usability of the two measures in practical situations.