To find the surface area of the trapezoidal prism, we need to evaluate the given expression:
[tex]\[ 6 \cdot 3 + 6 \cdot 4 + 6 \cdot 5 + 6 \cdot 8 + 2 \left( 3 \cdot 4 + \frac{1}{2} (3 \cdot 4) \right) \][/tex]
Let's break this down step-by-step.
1. Calculate each multiplication term individually:
[tex]\[
6 \cdot 3 = 18
\][/tex]
[tex]\[
6 \cdot 4 = 24
\][/tex]
[tex]\[
6 \cdot 5 = 30
\][/tex]
[tex]\[
6 \cdot 8 = 48
\][/tex]
2. Evaluate the expression inside the parentheses:
[tex]\[
3 \cdot 4 = 12
\][/tex]
Then find half of this value:
[tex]\[
\frac{1}{2} (3 \cdot 4) = \frac{1}{2} \cdot 12 = 6
\][/tex]
Sum these two results inside the parentheses:
[tex]\[
3 \cdot 4 + \frac{1}{2} (3 \cdot 4) = 12 + 6 = 18
\][/tex]
Multiply this result by 2:
[tex]\[
2 \left( 3 \cdot 4 + \frac{1}{2} (3 \cdot 4) \right) = 2 \cdot 18 = 36
\][/tex]
3. Add all the individual results together:
[tex]\[
18 + 24 + 30 + 48 + 36 = 156
\][/tex]
So, the surface area (S.A.) of the trapezoidal prism is:
[tex]\[
\boxed{156} \, \text{ft}^2
\][/tex]
