A thin triangle has vertices \((0, 0)\), \((1, 0)\) and \((0, 2).\) Let the density function at any given point on the triangle be represented by \(\rho (x, y) = 1+3x+y\). What is the mass of this triangle?

**Details and assumptions**

The density of a material is defined as \(\rho = \frac{m}{V}\), where \(\rho\) is the density, \(m\) is the mass and \(V\) is the volume.

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