1. Rise/Run, Pythagorean Theorem and Area
Calculating Roof Area
Rise/Run, Pythagorean Theorem and Area

2. Roof Problems: The Importance of Design

4. Uncommon problems

5. Trusses and Rafters

6. Basic Roof Styles

9. Our Building
The roof will have a 4/12 pitch

10. Roof Terminology

11. What are the steps to order materials
1. Determine slope
2. Calculate rise of roof
3. Calculate length of slope
4. Convert all measurements into inches (or feet)
5. Calculate area of roof
6. Calculate number of square
7. Multiply square by roofing material needs per square
8. Calculate sheathing needed

12. Step 1 Finding the rise of the roof
We will have wall dimensions for the building and the slope required.
We will be using a 4/12 “pitch”

13. Set up a proportion Calculate this by setting up a proportion.
Rise over run is 4/12.
10’ = 120” (10’ is ½ of the span)
The rise at the ridge of the roof is 40” from the top of the wall

15. Finding Slope Length Let’s Pythagorize! (Pythagorean The.)
A2 + B2 = C2
40” leg, 120” leg
The slope (hypotenuse) is approximately 126-1/2”

16. Length of the roof
convert the other 20 ft. wall length dimension into inches.
20’ x 12 = 240”

17. Finding Area L x W = A 240” x 126.5” = 30360 in2
Now convert to Feet: divide by 144

18. 30360” / 144 = 210 ft2
Now we need to figure the # of “squares” on the roof to order shingles
A square is 10’ x 10’ or 100 ft2
210 / 100 = 2.1 (number of squares)
We need to double that # because we have 2 sides of the roof to cover

19. Ordering shingles We have 4.2 square
3 bundles of shingles cover 1 square
How many bundles of shingles do we need?
4.2 x 3 = 12.6
Round up to AT LEAST 13

20. Estimating Roof Sheathing OSB or Plywood
420 sq. ft.
Each sheet of OSB is 4’ x 8’
What is the area of a sheet of OSB?
32 ft2

21. Calculating amount by 420 / 32 = 13.125
420 / 32 =
We need at least 14 sheets of OSB

22. Math Practice Questions
Find the pitch for the following roofs:
Total Rise Span Pitch
8’ 24’ 8/24 =1/3
6’ 36’
9’ ’
12’ ’
8’ ’

23. Total Rise Span Pitch
8’ 24’ 8/24 =1/3
6’ 36’ 6/36 =1/6
9’ ’ 9/24 =3/8
12’ ’ 12/36 = 1/3
8’ ’ 8/32 =1/4

24. Word problems
2. Ima Genius is trying to convince her dad to buy new carpet for her bedroom. The dimensions of her room are 10’ by 12’. How many square feet of carpet would her dad need to buy? Draw and label a diagram and solve showing your work.
3. Heeszo Smart (Ima’s cousin) decided to carpet his bedroom also. He found 3 dozen carpet samples at a garage sale. Each one measures 2’ by 2’. His room is 10’ by 14’. Does he have enough carpet samples? Explain.
Ima’s dad finds bundles of floor tiles at a yard sale. He bought 6 bundles of 10 tiles. Each tile is 16” by 16”. How many tiles will be needed to cover the floor of her room? Does he have enough tiles?