The x, y coordinates of the centre of mass of a uniform L-shaped lamina of mass 3 kg is

 

Choosing the x and y axes as shown in the figure. The coordinates of the vertices of the L-shaped lamina is as shown in the figure. Divide the L-shaped lamina into three squares each of side 1 m and mass 1 kg ($\because$ the lamina is uniform). By symmetry the centres of mass ${\mathrm{C}}_1, {\mathrm{C}}_2 \mathrm{and} {\mathrm{C}}_3$ of the squares are their geometric centres and have coordinates ${\mathrm{C}}_1(\frac{1}{2}, \frac{1}{2}), {\mathrm{C}}_2 (\frac{3}{2}, \frac{1}{2}) \mathrm{and} {\mathrm{C}}_3(\frac{1}{2}, \frac{3}{2})$ respectively.

The coordinates of the centre of mass of the L-shaped lamina is 

${\mathrm{X}}_{\mathrm{CM}} = \frac{{\mathrm{m}}_1{\mathrm{x}}_1+{\mathrm{m}}_2{\mathrm{x}}_2+{\mathrm{m}}_3{\mathrm{x}}_3}{{\mathrm{m}}_1+{\mathrm{m}}_2+{\mathrm{m}}_3}$

        = $\frac{1\times {\displaystyle \frac{1}{2}}+1\times {\displaystyle \frac{3}{2}}+1\times {\displaystyle \frac{1}{2}}}{1+1+1} = \frac{5}{6}\mathrm{m}$

${\mathrm{Y}}_{\mathrm{CM}} = \frac{{\mathrm{m}}_1{\mathrm{y}}_1+{\mathrm{m}}_2{\mathrm{y}}_2+{\mathrm{m}}_3{\mathrm{y}}_3}{{\mathrm{m}}_1+{\mathrm{m}}_2+{\mathrm{m}}_3}$

        = $\frac{1\times {\displaystyle \frac{1}{2}}+1\times {\displaystyle \frac{1}{2}}+1\times {\displaystyle \frac{3}{2}}}{1+1+1} = \frac{5}{6}\mathrm{m}$