To find the value of the remaining variable \( B \) in the formula for the area of a trapezoid, we can start by substituting the known values into the formula:
\[ A = \frac{1}{2}h(b + B) \]
Given:
- \( A = 30 \)
- \( h = 3 \)
- \( b = 14 \)
Substituting these values in:
\[ 30 = \frac{1}{2} \cdot 3 \cdot (14 + B) \]
Now, simplify the equation:
\[ 30 = \frac{3}{2} (14 + B) \]
To eliminate the fraction, multiply both sides by 2:
\[ 60 = 3(14 + B) \]
Next, divide both sides by 3:
\[ 20 = 14 + B \]
Now, solve for \( B \):
\[ B = 20 - 14 \] \[ B = 6 \]
Therefore, the value of the remaining variable \( B \) is \( \boxed{6} \).
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