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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