Where is the love?

Triangle A intersects with Triangle B and shares a common area of $30 \text{ m}^2$ . Triangle B shares a common area of $40\text{ m}^2$ with Triangle C, and Triangle C shares a common area of $50 \text{ m}^2$ with Triangle A. If all triangles have integer areas not greater than $60 \text{ m}^2$ , and that every triangle must have an area strictly of its own, what is the minimum sum of areas of the three triangles?