Assume you are working on a house the length of the house is 50 feet, the width is 30 feet, and from the ground to the gable is 10 feet. The height of the triangle prism on top is 6.5 feet. If you are going to shingle the roof of this house, how many square feet should you plan for?
Assuming no overhang at the eaves, the length of the roof is 50 ft and the width on each side is
w^2 = 15^2 + 6.5^2
w = 16.35
So, the area is 2 * 50 * 16.35 = 1635 ft^2
To calculate the total square footage of the roof that needs to be shingled, we need to find the areas of both the rectangular base and the triangular prism on top.
1. First, let's calculate the area of the rectangular base of the house:
Area = Length × Width
Length = 50 feet
Width = 30 feet
Area = 50 ft × 30 ft
Area = 1500 square feet
2. Now, let's calculate the area of the triangular prism on top of the house:
To find the area of a triangle, we can use the formula: (Base × Height) / 2
Base = Width of the house = 30 feet
Height = Height of the triangle prism = 6.5 feet
Area_triangular_prism = (Base × Height) / 2
Area_triangular_prism = (30 ft × 6.5 ft) / 2
Area_triangular_prism = 195 square feet
3. Finally, let's add the areas of the rectangular base and the triangular prism to find the total area of the roof:
Total area = Area of rectangular base + Area of triangular prism
Total area = 1500 square feet + 195 square feet
Total area = 1695 square feet
Therefore, you should plan for approximately 1695 square feet of shingles to cover the roof of this house.