1. **State the problem:** We are given a rectangle with width 16 cm and height 4 cm, and a square whose side length is unknown. The area of the rectangle is equal to the area of the square. 2. **Formula for area:** - Area of rectangle = width \times height - Area of square = side length \times side length = side length squared 3. **Calculate the area of the rectangle:** $$16 \times 4 = 64$$ cm² 4. **Set the area of the square equal to the area of the rectangle:** $$\text{side length}^2 = 64$$ 5. **Solve for the side length:** $$\text{side length} = \sqrt{64} = 8$$ cm 6. **Conclusion:** The side length of the square is 8 cm.