Cluster algebras were introduced by Fomin and Zelevinsky in the early 2000s, with the intent of establishing a general algebraic structure for studying dual canonical bases of semisimple groups and total positivity. A cluster algebra is a commutative ring determined by an initial “seed,” which consists of A-variables, X-variables, and some additional data. One then applies a combinatorial process called mutation to this seed to obtain another seed. The cluster algebra is generated by the variables obtained from all possible sequences of mutations. In this talk, we will focus on cluster algebras of finite type, which are those with finitely many A- and X-variables. There is a complete classification of finite type cluster algebras due to Fomin and Zelevinsky, which coincides with the classification of reduced crystallographic root systems. For classical types, the combinatorics of the A-variables and their mutations are encoded by triangulations of marked surfaces associated to each type. In particular, seeds are in bijection with triangulations, and A-variables are in bijection with the arcs of the triangulations. In this talk, we will discuss new results on the combinatorics of the X-variables in finite type cluster algebras. We will show that in classical types, the X-variables are in bijection with the quadrilaterals (with a choice of diagonal) appearing in triangulations of the surface of the appropriate type. Using this bijection, we can then count the number of X-variables in each type, as well as obtain some corollaries regarding the structure of finite type cluster algebras.