To solve for $b_1$ in the given equation:

$A = \frac{1}{2} (b_1 + b_2) h$

Steps:

1. Start by isolating $(b_1 + b_2)$: $2A = (b_1 + b_2) h$

2. Divide through by $h$ to further isolate $b_1 + b_2$: $\frac{2A}{h} = b_1 + b_2$

3. Finally, subtract $b_2$ from both sides to isolate $b_1$: $b_1 = \frac{2A}{h} - b_2$

Final Answer:

$b_1 = \frac{2A}{h} - b_2$

Would you like me to verify with specific values or clarify further?

Here are 5 related questions you might explore:

1. What is the geometric interpretation of this formula (e.g., area of a trapezoid)?
2. How does changing $h$ affect the value of $b_1$?
3. If $A$, $b_2$, and $h$ are known, how can this formula be applied practically?
4. How would the formula change if $A$ were multiplied by a constant?
5. Can you derive $b_2$ from the same formula?

Tip: When rearranging equations, always verify your steps by substituting back into the original formula.