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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 theintegral $A(p_1,p_2,p_3)=\int_\Sigma \omega$, where $\Sigma$ is a surfacefilling 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 threepoints, we prove an explicit formula for $A(p_1,p_2,p_3)$ analogous to theknown formula for the symplectic area of a geodesic triangle in a non-compactHermitian symmetric space.

The symplectic area of a geodesic triangle in a Hermitian symmetric space of compact type