Give the definition for the area of a hyperbolic triangle with interior angles $\alpha, \beta, \gamma$.

Let $n \geqslant 3$. Show that the area of a convex hyperbolic $n$-gon with interior angles $\alpha_{1}, \ldots, \alpha_{n}$ is $(n-2) \pi-\sum \alpha_{i}$.

Show that for every $n \geqslant 3$ and for every $A$ with $0<A<(n-2) \pi$ there exists a regular hyperbolic $n$-gon with area $A$.