  Let $M$ be an irreducible Hermitian symmetric space of compact type, and let
$\omega$ be its K\"ahler form. For a triplet $(p_1,p_2,p_3)$ of points in $M$
we study conditions under which a geodesic triangle $\mathcal T(p_1,p_2,p_3)$
with vertices $p_1,p_2,p_3$ can be unambiguously defined. We consider the
integral $A(p_1,p_2,p_3)=\int_\Sigma \omega$, where $\Sigma$ is a surface
filling the triangle $\mathcal T(p_1,p_2,p_3)$ and discuss the dependence of
$A(p_1,p_2,p_3)$ on the surface $\Sigma$. Under mild conditions on the three
points, we prove an explicit formula for $A(p_1,p_2,p_3)$ analogous to the
known formula for the symplectic area of a geodesic triangle in a non-compact
Hermitian symmetric space.
