Suppose I have $n$ areas of masses $m_1, m_2, ... ,m_n$, each with a center of mass $[x_i, y_i]$. They have no intersections between them - the areas are exclusive.
If I consider them all as one body (one area), what is their center of mass? Is it this:
$$x = \frac{\sum_{i=0}^n m_ix_i}{\sum_{i=0}^n m_i}$$ ?
Yes, you may consider such model. Your formula is true.