To solve for \( b \) in the equation \( A = \frac{1}{2}(a + b) \), we can start by multiplying both sides of the equation by 2 to eliminate the fraction:
\[ 2A = a + b \]
Next, we want to isolate \( b \). To do this, we can subtract \( a \) from both sides:
\[ b = 2A - a \]
So, the solution for \( b \) is:
\[ \boxed{b = 2A - a} \]