The perimeter of a square can be calculated using the formula:

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

Given the side length of the square is $9 \frac{1}{2}$ cm, we first express this as a fraction:

$9 \frac{1}{2} = \frac{19}{2} \text{ cm}$

Now, calculate the perimeter:

$\text{Perimeter} = 4 \times \frac{19}{2} = \frac{76}{2} = 38 \text{ cm}$

Thus, the perimeter of the square is 38 cm.

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Would you like a more detailed explanation or have any questions? Here are some related questions you might find interesting:

1. How do you calculate the area of a square?
2. What would be the perimeter of a square if the side length were doubled?
3. How does the perimeter of a square relate to the perimeter of a rectangle?
4. What is the diagonal length of a square given the side length?
5. How can you find the side length of a square if you know its perimeter?

Tip: Always convert mixed numbers into improper fractions for easier calculations!