Confined electronic states and optical transitions in 3D topological insulator nanoparticles have been studied in the literature, assuming idealized geometries such as spheres or infinitely long cylinders, that allow to obtain analytical solutions to the corresponding eigenvalue equation within such geometries. In contrast, in this article we consider triangular-shaped nanoplates as a more realistic approximation to the experimentally observed morphologies of topological insulator nanoparticles. In this particular geometry, we obtain analytical expressions for the confined eigenstates and the corresponding energy spectrum. Moreover, by a spatial representation of the probability density distribution, we further identify the conditions leading to the emergence of topologically trivial surface states, i.e. those arising as a result of morphological-dependent quantum confinement of the bulk that nonetheless project onto the surface, in contrast with topologically protected surface states. Finally, we also study the optical transitions and the corresponding selection rules imposed by the nanoparticle size and morphology.