For a roof slope of 4 in 12, the factor to convert plan area to actual area is

For a roof slope of 4 in 12, the factor to convert plan area to actual area is

• A. 1.014
• B. 1.031
• C. 1.054
• D. 1.083

Answer: (C)

Sloped roof surfaces are larger than their horizontal plan area because the surface is inclined. The conversion factor from plan area to actual roof area is the secant of the roof angle, which can be found from the rise/run of the slope: factor = sqrt(1 + (rise/run)^2). For a 4 in 12 pitch, rise/run = 4/12 = 1/3. So the factor is sqrt(1 + (1/3)^2) = sqrt(1 + 1/9) = sqrt(10/9) = sqrt(10)/3 ≈ 1.054. Therefore, the factor is about 1.054.

Sloped roof surfaces are larger than their horizontal plan area because the surface is inclined. The conversion factor from plan area to actual roof area is the secant of the roof angle, which can be found from the rise/run of the slope: factor = sqrt(1 + (rise/run)^2).

For a 4 in 12 pitch, rise/run = 4/12 = 1/3. So the factor is sqrt(1 + (1/3)^2) = sqrt(1 + 1/9) = sqrt(10/9) = sqrt(10)/3 ≈ 1.054. Therefore, the factor is about 1.054.