Given a roof slope of 3 in 12, what factor should be used to convert the plan area to actual roof area?

To determine the factor used to convert the plan area to the actual roof area for a slope of 3 in 12, you first need to understand how roof pitch affects the area. The slope of 3 in 12 means that for every 12 horizontal units, the roof rises 3 vertical units.

To calculate the actual roof area factoring in the slope, you use the Pythagorean theorem. The total length of the "rise" and "run" can be calculated as follows:

1. The horizontal run is 12 units.

2. The vertical rise is 3 units.

3. The sloped length (hypotenuse) can be calculated using the formula:

( \text{hypotenuse} = \sqrt{(\text{run})^2 + (\text{rise})^2} )

( \text{hypotenuse} = \sqrt{(12)^2 + (3)^2} )

( \text{hypotenuse} = \sqrt{144 + 9} )

( \text{hypotenuse} = \sqrt{153} )

( \text{hypotenuse} \approx 12.37 )