To calculate the area of the square, we first need to find the length of one of its sides.

Step 1: Use the perimeter formula of a square.

The perimeter $P$ of a square is given by the formula:

$P = 4 \times \text{side length}$

Given that the perimeter is 32 cm, we can solve for the side length:

$32 = 4 \times \text{side length}$

$\text{side length} = \frac{32}{4} = 8 \, \text{cm}$

Step 2: Calculate the area.

The area $A$ of a square is given by the formula:

$A = \text{side length}^2$

Substitute the side length:

$A = 8^2 = 64 \, \text{sq. cm}$

Final Answer:

The area of the square is 64 square centimeters.

Would you like further details on how to approach such problems? Or do you have any other questions?

Related Questions:

1. How do you find the side length of a square when given the area?
2. What is the difference between the perimeter and area of a square?
3. How would you find the perimeter if you know the area of a square?
4. What is the formula for the diagonal of a square?
5. How does the area of a square compare to the area of a rectangle with the same perimeter?

Tip: Remember, the perimeter of a square always gives you a way to find the side length, which is key for calculating the area.