1. **State the problem:** We need to find the lateral surface area of a rectangular prism with dimensions 7.5 in. (length), 5 in. (width), and 6.5 in. (height). 2. **Formula for lateral surface area:** The lateral surface area (LSA) of a rectangular prism is the sum of the areas of the four vertical faces (excluding the top and bottom). It is given by: $$\text{LSA} = 2h(l + w)$$ where $h$ is the height, $l$ is the length, and $w$ is the width. 3. **Substitute the given values:** $$\text{LSA} = 2 \times 6.5 \times (7.5 + 5)$$ 4. **Simplify inside the parentheses:** $$7.5 + 5 = 12.5$$ So, $$\text{LSA} = 2 \times 6.5 \times 12.5$$ 5. **Multiply step-by-step:** $$2 \times 6.5 = 13$$ So, $$\text{LSA} = 13 \times 12.5$$ 6. **Calculate the final product:** $$13 \times 12.5 = 162.5$$ 7. **Answer:** The lateral surface area of the prism is **162.5 square inches**. This means the total area of the four vertical faces (excluding top and bottom) is 162.5 in².