Rise/Run, Pythagorean Theorem and Area

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Presentation transcript:

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

Roof Problems: The Importance of Design

Uncommon problems

Trusses and Rafters

Basic Roof Styles

Our Building The roof will have a 4/12 pitch

Roof Terminology

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

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”

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

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

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

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

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

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

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

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

Math Practice Questions Find the pitch for the following roofs: Total Rise Span Pitch 8’ 24’ 8/24 =1/3 6’ 36’ 9’ 24’ 12’ 36’ 8’ 32’

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

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. 4. 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?