1. The problem asks for the expression representing the total surface area of a rectangular prism with dimensions 5 cm, 4 cm, and 7 cm. 2. The formula for the total surface area $SA$ of a rectangular prism with length $l$, width $w$, and height $h$ is: $$SA = 2(lw + lh + wh)$$ This formula accounts for the area of all six faces: two each of $lw$, $lh$, and $wh$. 3. Substitute the given dimensions $l=5$, $w=4$, and $h=7$ into the formula: $$SA = 2(5 \times 4 + 5 \times 7 + 4 \times 7)$$ 4. Calculate each product inside the parentheses: $$5 \times 4 = 20$$ $$5 \times 7 = 35$$ $$4 \times 7 = 28$$ 5. Sum these values: $$20 + 35 + 28 = 83$$ 6. Multiply by 2 to get the total surface area: $$SA = 2 \times 83 = 166$$ 7. Therefore, the total surface area of the prism is 166 square centimeters. 8. Among the given options, the expression that matches the surface area formula is: $$2(5 \cdot 7) + 2(4 \cdot 7) + 2(4 \cdot 5)$$ which is equivalent to the correct formula. Final answer: $$2(5 \cdot 7) + 2(4 \cdot 7) + 2(4 \cdot 5)$$