To solve the equation \( A = \frac{1}{2} h (b + c) \) for \( b \), follow these steps:

1. **Multiply both sides by 2** to eliminate the fraction:
   \[
   2A = h(b + c)
   \]

2. **Divide both sides by \( h \)** to isolate \( b + c \) on one side:
   \[
   \frac{2A}{h} = b + c
   \]

3. **Subtract \( c \) from both sides** to solve for \( b \):
   \[
   b = \frac{2A}{h} - c
   \]

So, the solution for \( b \) is:
\[
b = \frac{2A}{h} - c
\]

Would you like more details on any part of this process, or do you have any other questions?

Here are 5 related questions to expand your understanding:
1. What happens if \( h = 0 \) in the original equation?
2. How would the solution change if the equation were \( A = \frac{1}{2}h(b - c) \)?
3. How would you solve the equation if \( c \) were unknown instead of \( b \)?
4. Can you express \( h \) in terms of \( A \), \( b \), and \( c \) from the original equation?
5. How does the solution change if the equation were in a different form, such as \( A = \frac{1}{2}(bh + ch) \)?

**Tip:** When solving for a variable, always perform the same operation on both sides of the equation to maintain equality.

Learn how to solve the equation A = (1/2)h(b + c) for variable b with a step-by-step solution. This problem covers algebraic concepts such as equation manipulation and variable isolation. Suitable for high school students.

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