To calculate the area of a square, we use the formula:

$\text{Area of a square} = \text{side length}^2$

Given that the side length of the square is $4 \, \text{cm}$:

$\text{Area of the square} = 4^2 = 16 \, \text{cm}^2$

Final Answer:

The area of the square is 16 square centimeters.

Would you like me to elaborate further? Here are some related questions to expand your understanding:

1. How does the area formula for a square compare to that of a circle?
2. What is the perimeter of the square with a side length of 4 cm?
3. If the side length of the square doubles, what will its new area be?
4. How would the area change if the square is inscribed within a circle of radius 4 cm?
5. Can a square with the same area fit inside a circle with a radius of 4 cm?

Tip: The area of a square grows quadratically with its side length, meaning even small increases in the side length significantly impact the area.