Use area integration to calculate the centre of mass of a triangle with vertices at (0, 0),(0, 1), (2, 0).(a)(i)[10 marks] Hence find the centre of mass of the object(ii)shown

in the diagram below (you may assume that the centre of mass of a rectangle is located at the midpoints of both sides). You may use the \text { result } \overline{\mathbf{r}}=\frac{1}{S} \sum_{i=1}^{n} S_{i} \overline{\mathbf{r}}_{i} \text { . } Find the mass of the unit cube occupying the region 0 \leq x \leq 1,0 \leq y \leq 1,0 \leq z \leq 1, \text { With density } \rho(x, y, z)=x^{2}+2 x y^{2}+z