There are two ways to define a sloped roof area: the surface area of the roof itself and the area protected by the roof. These have different areas because the roof lies on the hypotenuse of a triangle, whereas the area protected by it is horizontal. When determining sloped roof area for rainfall catchment, for example, you calculate the area protected by the roof, but when replacing the tiles you calculate the surface area of the roof itself.
Things You'll Need
- Tape measure
Determine the area protected by the sloping roof by multiplying the length of the roof by the width. The result is the area covered by the sloping roof. For example, a single sloping roof covering a house 30 feet long and 20 feet wide covers an area of 600 square feet -- 30 x 20 = 600. If the same house had a central roof-ridge dividing the roof into two sloping areas, each would cover 300 square feet or half the house.
Determine the surface area of the roof by first measuring the distance along an imaginary horizontal line from the edge of the roof to a spot vertically beneath the highest point. This is the base of the triangle. Record the distance.
Determine the difference in height between the lowest and the highest points on the roof. These are usually the points where the roof meets the house side walls and where it reaches the central roof ridge. Deduct the greater height from the lesser one to determine the height of the roof. This is the vertical side of the triangle. For example, if the roof ridge is 25 feet above ground level and the lower edge of the roof is 20 feet above ground level the vertical difference is 5 feet: 25 - 20 = 5.
Substitute the width and height determined in Step 2 and 3 into the Pythagorean Theorem which states that a^2 + b^2 = c^2, where a and b are the base and vertical sides of a triangle, and c is the hypotenuse. Solve the equation to determine the sloping width of the roof. For example, if the horizontal width is 10 feet and the height is 5 feet, the hypotenuse is 11.18 feet -- 10^2 + 5^2 = 125. The square root of 125 is 11.18.
Multiply the hypotenuse by the length of the roof. The result is the surface area of the sloping roof. For example, if the sloping surface is 11.18 feet wide, and the roof is 30 feet long, the sloping area is 335.4 square feet -- 11.18 x 30 = 335.4.