To find the area of a square when two sides lie on the given lines, we need to determine the perpendicular distance between these lines, as they represent parallel sides of the square. Here are the detailed steps:

1. The lines given are:
   • 2x + y - 3 = 0 (Line 1)
   • 4x + 2y + 5 = 0 (Line 2)
2. Both lines need to be rewritten to show they are parallel. Simplify Line 2:
   • Divide the entire equation by 2: 2x + y + 2.5 = 0 (Line 2 simplified)
3. Comparing both lines, we see they have the same slope (coefficients of x and y are proportional: \frac{2}{1} = \frac{2}{1}), confirming they are parallel.
4. The perpendicular distance d between two parallel lines Ax + By + C_1 = 0 and Ax + By + C_2 = 0 is given by: d = \frac{|C_2 - C_1|}{\sqrt{A^2 + B^2}}
5. Substitute the values:
   • C_1 = -3 and C_2 = 2.5
   • Perpendicular distance: d = \frac{|2.5 + 3|}{\sqrt{2^2 + 1^2}} = \frac{5.5}{\sqrt{5}}
6. Simplify the expression:
   • d = \frac{5.5}{\sqrt{5}} = \frac{5.5 \times \sqrt{5}}{5} = \frac{5.5\sqrt{5}}{5}
7. Approximate the value of \sqrt{5} \approx 2.236:
   • Substitute back to get: d \approx \frac{5.5 \times 2.236}{5} = \frac{12.298}{5} = 2.4596
8. The area of the square is the square of the side length: d^2 \approx (2.4596)^2 \approx 6.05.

Thus, the area of the square is approximately 6.05 square units.