What is the square foot area of the ventilation duct described as 32 feet long, 4 feet wide, and 3 feet 6 inches high, assumed open-ended and insulated?

• A. 508 sq ft
• B. 1792 sq ft
• C. 512 sq ft
• D. 480 sq ft

Answer: (B)

Calculating the amount of surface area to insulate focuses on the sides of the duct, because open ends aren’t insulated in this setup. The cross-section is 4 ft by 3.5 ft, so its perimeter is 2 × (4 + 3.5) = 15 ft. The surface area of the four walls is this perimeter times the length: 15 × 32 = 480 square feet. Since the ends are open, they aren’t part of the insulated area. If the ends were insulated too, you would add 2 × (width × height) = 2 × (4 × 3.5) = 28, giving 508 square feet. Here, the insulation area is 480 square feet.