The coordinates of the centre of mass of a uniform flag-shaped lamina (thin flat plate) of mass 4 kg. (The coordinates of the same are shown in the figure) are:

Divide the lamina into two rectangles: a vertical strip $$R_1$$ and a square flag piece $$R_2$$.

Vertical strip $$R_1$$ bounded by vertices $$(0,0)$$, $$(1,0)$$, $$(1,2)$$, $$(0,2)$$:

$$\text{Area } A_1 = 1 \times 2 = 2, \quad \text{Center of mass } (x_1, y_1) = (0.5, 1.0)$$

Square flag piece $$R_2$$ bounded by vertices $$(0,2)$$, $$(2,2)$$, $$(2,3)$$, $$(0,3)$$:

$$\text{Area } A_2 = 2 \times 1 = 2, \quad \text{Center of mass } (x_2, y_2) = (1.0, 2.5)$$

X-coordinate of the center of mass: $$x_{\text{cm}} = \frac{A_1 x_1 + A_2 x_2}{A_1 + A_2} = \frac{2(0.5) + 2(1.0)}{2 + 2} = \frac{1 + 2}{4} = 0.75\text{ m}$$

Y-coordinate of the center of mass: $$y_{\text{cm}} = \frac{A_1 y_1 + A_2 y_2}{A_1 + A_2} = \frac{2(1.0) + 2(2.5)}{2 + 2} = \frac{2 + 5}{4} = 1.75\text{ m}$$