The given equation is:

\[
A = \frac{1}{2}s^2
\]

We are tasked with finding \( s \). To do this, we'll solve for \( s \) step by step.

### Step 1: Multiply both sides by 2 to eliminate the fraction.

\[
2A = s^2
\]

### Step 2: Take the square root of both sides to solve for \( s \).

\[
s = \pm \sqrt{2A}
\]

Thus, the solution for \( s \) is:

\[
s = \pm \sqrt{2A}
\]

The \( \pm \) sign indicates that there are two possible values for \( s \), one positive and one negative.

Would you like more details or any clarifications?

Here are 5 related questions to consider:
1. If \( A = 4 \), what are the possible values for \( s \)?
2. How would the solution change if \( A \) was negative?
3. Can you derive the units of \( s \) if \( A \) has specific units?
4. What is the geometric interpretation of this equation?
5. How does the formula \( A = \frac{1}{2}s^2 \) relate to the formula for kinetic energy?

**Tip:** Always check both the positive and negative solutions when taking square roots in equations.

This solution provides a step-by-step guide on solving the equation A = 1/2 s^2 for s. It explores algebraic methods, the square root theorem, and related formulas. Perfect for students in Grades 9-12.

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