Isabella's house has bedrooms. Each bedroom is feet long, feet wide, and feet high. Isabella must paint the walls of all the bedrooms. Doorways and windows, which will not be painted, occupy square feet in each bedroom. How many square feet of walls must be painted?
- A)
- B)
- C)
- D)
- E)
Answer
E
Key insight
Each room's four walls form a band of perimeter 44 feet and height 8 feet; subtract the 60 square feet of openings, then triple.
Solution
Only the four walls of each room are painted, not the floor or ceiling. Unrolled, the four walls form one long rectangle whose width is the perimeter of the floor and whose height is feet:
Remove the doors and windows: square feet per bedroom.
Three bedrooms: .
The answer is .
Why this works
The lateral surface of a box is perimeter times height; thinking of the walls as one strip avoids adding four rectangles separately. Subtract the unpainted openings per room before scaling up, and read carefully which surfaces are actually painted.
The trap
Including the floor or ceiling in the painted area, or forgetting to multiply by three bedrooms.
Common mistakes
- Including the floor or ceiling in the painted area, or forgetting to multiply by three bedrooms.
- Subtracting only once instead of once per bedroom, giving .
- Transposing digits under time pressure: , and are all offered as distractors.
Techniques
Set up the equation/formula and compute; no special trick needed