A gable roof with a slope of 9 inches per foot has a rake slope factor of 1.25. If the run is 10 feet and the eaves length is 30 feet. What is the roof area in sq feet. a 150 b 1500 c 300 or d 750
To calculate the roof area, you first need to determine the length of the roof ridge.
Given that the run is 10 feet and the slope is 9 inches per foot, you can find the rise using the formula: Rise = Run x Slope = 10 ft x (9 in/12 in) = 7.5 ft.
Next, calculate the length of the roof ridge by using the Pythagorean theorem, which states that the square of the hypotenuse (ridge length) is equal to the sum of the squares of the other two sides (eaves length and rise):
Ridge Length^2 = Eaves Length^2 + Rise^2
Ridge Length^2 = 30 ft^2 + 7.5 ft^2 = 900 ft^2 + 56.25 ft^2 = 956.25 ft^2
Ridge Length ≈ √956.25 ft^2 ≈ 30.99 ft (rounded to the nearest hundredth)
Now, you can calculate the roof area by multiplying the run, the eaves length, and the rake slope factor:
Roof Area = Run x Eaves Length x Rake Slope Factor = 10 ft x 30 ft x 1.25 = 375 sq ft.
Therefore, the correct answer is d) 750 sq ft.
To find the roof area of a gable roof, we need to calculate the area of each triangular face and then add them together.
First, let's find the length of the ridge. The ridge is the topmost horizontal line connecting the two ends of the gable roof. In this case, the run is given as 10 feet.
The rake slope factor determines the slope of the roof at the gable end. It is given as 1.25, which means for every foot horizontally, the roof rises by 1.25 feet vertically. Since the run is 10 feet, we can calculate the rise using the slope factor:
Rise = Run * Slope Factor
Rise = 10 * 1.25
Rise = 12.5 feet
Now let's find the length of the ridge. The length of the ridge is the same as the eaves length, which is given as 30 feet.
Now, we can calculate the area of each triangular face using the formula:
Area = (Base * Height) / 2
Area of one triangular face = (Run * Rise) / 2
Area of one triangular face = (10 * 12.5) / 2
Area of one triangular face = 125 square feet
Since there are two triangular faces in a gable roof, we need to multiply the area of one triangular face by 2 to get the total roof area:
Total Roof Area = Area of one triangular face * 2
Total Roof Area = 125 * 2
Total Roof Area = 250 square feet
Therefore, the roof area is 250 square feet.
If the slope is 9 inches per foot (run), then the roof is 15" per foot run.
I suppose rake factor is the ratio of roof length to rise, which works out to 1.25 in this case.
The roof area (for one sloping face) is therefore
(15"/9")*10'*30' long
= 500 sq. ft.
If the roof has another sloping face, then double the above.