Final answer:
The question involves calculating squares of shingles for a gable roof in terms of mathematics. It includes measuring the house dimensions, considering the pitch of the roof, extending for overhangs, and converting the area to roofing squares calculation.
Step-by-step explanation:
The calculation of how many squares of shingles needed for a roof is a practical application of mathematics in a real-world context.
The roof of the home measures 28'(length)x40'(width) with a 6/12 gable roof and a 1' overhang on all ends. To find the total area, we need to calculate the area of both sides of the gable roof.
For each side of the gable roof, consider it as two right triangles and a rectangle in between.
The width of this roof section will be the same as the width of the house, 40', plus 2' for the overhang on both ends.
The total span becomes 42'. The height of the triangle (or the rise) can be found by applying the roof's pitch, which is a 6/12 pitch.
This means that for every 12' horizontally, the roof rises 6'. Half of the 40' width is 20', so (6/12) * 20' = 10' is the rise.
Use this to calculate the area of the triangles (1/2 base * height) and add the area of the rectangle (the span of the roof by the length of the house).
To calculate the total square footage, multiply the area by 2 (since there are two sides to the roof), and then divide by 100 to convert from square feet to roofing squares (since one roofing square equals 100 square feet).
Remember to add extra for waste, usually estimated at around 10-15% on top of the calculated area, especially with gable roofs where cuts result in more waste. Given that the roof has a simple shape, the lower end of additionally required squares is reasonable.