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

1. Start with the given formula:
   \[
   A = \frac{1}{2}h(a + b)
   \]

2. Multiply both sides of the equation by 2 to eliminate the fraction:
   \[
   2A = h(a + b)
   \]

3. Divide both sides by \( h \) to isolate \( a + b \):
   \[
   \frac{2A}{h} = a + b
   \]

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

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

Would you like more details or have any questions?

Here are 5 related questions to expand on this:

1. How would you solve for \( a \) instead of \( b \)?
2. What is the geometric interpretation of this equation?
3. How would this equation change if the coefficient \( \frac{1}{2} \) were different?
4. Can this formula be applied to find the area of a trapezoid?
5. How would you modify the equation if \( A \) represented a different shape?

**Tip**: When solving for a variable, it's helpful to isolate the variable step by step, keeping track of operations applied to both sides of the equation.

Learn how to solve for b in the formula A = (1/2)h(a + b) with a clear step-by-step algebraic solution. This example focuses on solving for variables, linear equations, and basic algebraic operations. Suitable for students in Grades 8-10.

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