To solve this problem, we need to calculate the lateral surface area of the rectangular prism. The lateral surface area is the total area of all the vertical sides of the prism.

Steps:

1. Identify the dimensions:

   • Length ($l$) = 7 ft
   • Width ($w$) = 3 ft
   • Height ($h$) = 5 ft

2. Calculate the lateral surface area: The lateral surface area (LSA) of a rectangular prism is calculated using the formula: $\text{LSA} = 2 \cdot h \cdot (l + w)$ Substituting the given dimensions: $\text{LSA} = 2 \cdot 5 \cdot (7 + 3)$ Simplify: $\text{LSA} = 2 \cdot 5 \cdot 10 = 100 \, \text{ft}^2$

Final Answer:

The lateral surface area of the prism is 100 square feet.

Would you like a detailed explanation of any part of the solution or have additional questions?

Here are five related questions to deepen your understanding:

1. How is the total surface area of the rectangular prism different from the lateral surface area?
2. What would be the lateral surface area if the height was doubled?
3. How would the formula change for a triangular prism?
4. Can the same formula be used for a cylinder? Why or why not?
5. What is the significance of lateral surface area in real-world applications like packaging?

Tip: Always double-check the dimensions and the specific surfaces you need to calculate to avoid errors.