1. Problem: Find the ratio of areas of two squares with given side lengths. 2. Formula: The ratio of areas of two squares is the square of the ratio of their corresponding side lengths, i.e., $$\frac{A_1}{A_2} = \left(\frac{l_1}{l_2}\right)^2$$. 3. Calculations: (a) Side lengths: 6 mm and 4 mm $$\frac{A_1}{A_2} = \left(\frac{6}{4}\right)^2 = \left(1.5\right)^2 = 2.25$$ (b) Side lengths: 4.8 m and 3.6 mm (convert 3.6 mm to meters: 0.0036 m) $$\frac{A_1}{A_2} = \left(\frac{4.8}{0.0036}\right)^2 = \left(1333.33\right)^2 = 1777777.78$$ (c) Side lengths: 10 mm and 1.5 mm $$\frac{A_1}{A_2} = \left(\frac{10}{1.5}\right)^2 = \left(6.6667\right)^2 = 44.44$$ (d) Side lengths: 1.5 m and 40 cm (convert 40 cm to meters: 0.4 m) $$\frac{A_1}{A_2} = \left(\frac{1.5}{0.4}\right)^2 = \left(3.75\right)^2 = 14.06$$ Final answers: (a) 2.25 (b) 1777777.78 (c) 44.44 (d) 14.06 These results show that the ratio of areas is the square of the ratio of side lengths.