How many square feet of plywood is required to sheath a plain gable roof on a 26' x 54' building with a 2' overhang and a slope of 3-in-12?

To determine the amount of plywood required to sheath a plain gable roof, first, we need to calculate the total area of the roof that needs to be covered.

1. Calculate the dimensions of the roof: The building is 26 feet wide and 54 feet long. The roof has a 2-foot overhang on each side, which adds 4 feet to the total width. Therefore, the total width of the roof is 26 + 4 = 30 feet.

2. Determine the slope of the roof: The slope of 3-in-12 means that for every 12 horizontal feet, the roof rises 3 feet. To find the rise over the width of the building, you can use a right triangle representation of the roofing.

3. Calculate the run for the half-roof: Since it’s a gable roof, we consider half the width to find the run. Half of 30 feet is 15 feet. The rise for 15 feet horizontal distance using the slope 3-in-12 can be calculated as follows:

[

\text{Rise} = \left(\frac{3}{12}\right) \times 15 = 3.75