For a real K3-surface X , one can introduce areas of connected components of the real point set \mathbb{R}X of X using a holomorphic symplectic form of X . These areas are defined up to simultaneous multiplication by a positive real number, so the areas of different components can be compared. In particular, it turns out that the area of a non-spherical component of \mathbb{R}X is always greater than the area of any spherical component. In this paper we explore further comparative restrictions on the area for real K3-surfaces admitting a suitable polarization of degree 2g - 2 (where g is a positive integer) and such that \mathbb{R}X has one non-spherical component and at least g spherical components. For this purpose we introduce and study the notion of simple Harnack curves in real K3-surfaces, generalizing planar simple Harnack curves from [8].