\begin{tabular}{l} (4)) Which expression represents the total \ surface area of the prism shown? \ $$ 4(5)+4(7)+5(7) $$ \ $$ 2(4 \cdot 4)+2(5 \cdot 5)+2(7 \cdot 7) $$ \ $$ 4(4)+5(5)+7(7) $$ \ $$ 2(5 \cdot 7)+2(4 \cdot 7)+2(4 \cdot 5) $$ \ \hline\end{tabular}

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We are given a prism with dimensions $$4$$, $$5$$, and $$7$$. For a rectangular prism, the total surface area (TSA) is calculated using the formula

$$
\text{TSA} = 2(\text{length} \times \text{width}) + 2(\text{length} \times \text{height}) + 2(\text{width} \times \text{height})
$$

Substituting the given dimensions:

$$
\text{TSA} = 2(4 \times 5) + 2(4 \times 7) + 2(5 \times 7)
$$

We see that this expression corresponds to the option

$$
2(5 \cdot 7) + 2(4 \cdot 7) + 2(4 \cdot 5)
$$
The correct expression for the total surface area of the prism is $$2(5 \cdot 7) + 2(4 \cdot 7) + 2(4 \cdot 5)$$.

(4)) Which expression represents the total

surface area of the prism shown?

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(4)) Which expression represents the total surface area of the prism shown?