Question

Find the value of the remaining variable in the formula.
A =1/2h(b+B)
​(area of a​ trapezoid);  A =30​, h=3​, b=14

Answer 1

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 \( \boxed{6} \).