Directions for questions : Select the correct answer from the given options.
If `A = S^(2) and A = 324 "cm"^2`, then find the value of S (in cm).

Options

A. 162
B. `(324)^2`
C. `18`
D. `16`

Answer

To solve the problem, we need to find the value of \( S \) given that \( A = S^2 \) and \( A = 324 \, \text{cm}^2 \).

### Step-by-Step Solution:

1. **Write down the formula**: We know that the area \( A \) is given by the formula:
\[ A = S^2 \]

2. **Substitute the value of \( A \)**: We are given that \( A = 324 \, \text{cm}^2 \). So we can substitute this into the formula:
\[ 324 = S^2 \]

3. **Solve for \( S^2 \)**: Now, we need to find \( S \) by isolating \( S^2 \):
\[ S^2 = 324 \]

4. **Take the square root of both sides**: To find \( S \), we take the square root of both sides of the equation:
\[ S = \sqrt{324} \]

5. **Calculate the square root**: We can simplify \( \sqrt{324} \):
- We know that \( 18 \times 18 = 324 \), so:
\[ S = 18 \, \text{cm} \]

### Final Answer:
The value of \( S \) is \( 18 \, \text{cm} \).