A contractor is preparing an estimate for a roof with a flat plan (footprint) area of 3,200 square feet and a slope of 7:12. What is the approximate actual surface area of the roof, considering the slope?
- A3,910 sq ft
- B3,200 sq ft
- C3,467 sq ft
- D3,733 sq ft
Show answer & explanationAnswer & explanation
Correct answer: D. 3,733 sq ft
For a 7:12 slope, the slope factor is approximately 1.166. Multiply the flat plan area by this factor: 3,200 sq ft * 1.166 = 3,731.2 sq ft. The closest answer is 3,733 sq ft. (Calculation of slope factor: sqrt(7^2 + 12^2) / 12 = sqrt(49 + 144) / 12 = sqrt(193) / 12 = 13.892 / 12 = 1.1577. 3200 * 1.1577 = 3704.64. Using a common table value for 7:12, it's often rounded to 1.167 or 1.17.) Let's re-evaluate with standard factors. A 7:12 slope typically has a factor of 1.158 or 1.16. Using 1.16: 3200 * 1.16 = 3712. Let's use the exact calculation: sqrt((7^2) + (12^2)) / 12 = sqrt(49 + 144) / 12 = sqrt(193) / 12 = 13.8924 / 12 = 1.1577. 3200 * 1.1577 = 3704.64 sq ft. Option C is the closest.
Why the other options are wrong
- A. This would correspond to a steeper slope, such as 8:12 or 9:12.
- B. This is the flat plan area, not the actual surface area adjusted for slope.
- C. This would correspond to a shallower slope, such as 5:12 or 6:12.
Slope Factor Application
The use of a slope factor to convert a roof's flat plan (footprint) area into its actual surface area, which is necessary for accurate material takeoffs.
- Slope factors account for the increased surface area due to roof pitch.
- Different pitches (rise:run) have different slope factors.
- Actual surface area is always greater than or equal to the flat plan area.
Memory trick: Slope Factor is the trick to true roof area, don't miss the rise!