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

### Step 1: Eliminate the fraction
Multiply both sides of the equation by 2 to get rid of the fraction:

\[
2A = h(a + b)
\]

### Step 2: Divide by \( h \)
To isolate \( a + b \), divide both sides by \( h \):

\[
\frac{2A}{h} = a + b
\]

### Step 3: Solve for \( a \)
Subtract \( b \) from both sides to solve for \( a \):

\[
a = \frac{2A}{h} - b
\]

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

\[
a = \frac{2A}{h} - b
\]

Would you like further details or have any questions?

### Related questions:
1. How can this formula be applied in geometry, like finding the area of a trapezoid?
2. What is the significance of the variable \( h \) in this equation?
3. How does this formula change if \( A \) represents volume instead of area?
4. Can you substitute specific values for \( A \), \( h \), and \( b \) to find \( a \)?
5. What happens if \( h \) is equal to zero?

**Tip:** When solving for a variable, always aim to isolate it step-by-step by performing inverse operations.

Learn how to solve the equation A = 1/2h(a + b) for the variable 'a'. This problem explores algebraic manipulation, solving for a specific variable, and basic geometric concepts like areas. Suitable for students in Grades 8-10.

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