The Area of Convex Projective Surfaces and Fock-Goncharov Coordinates

The area of a convex projective surface of genus $g\ge 2$ is at least $(g-1)\pi^2/2+\|\tau\|^2/8$ where $\tau=(\log t_i)$ is the vector of triangle invariants of Bonahon-Dreyer and $t_i$ are the Fock-Goncharov triangle coordinates.