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 (∵ the lamina is uniform). By symmetry the centres of mass C1, C2 and C3 of the squares are their geometric centres and have coordinates C1(12, 12), C2 (32, 12) and C3(12, 32) respectively.The coordinates of the centre of mass of the L-shaped lamina is XCM = m1x1+m2x2+m3x3m1+m2+m3        = 1×12+1×32+1×121+1+1 = 56mYCM = m1y1+m2y2+m3y3m1+m2+m3        = 1×12+1×12+1×321+1+1 = 56m