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?

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.

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.