1. Roofing Materials Estimating

2. A square is used to describe an area of roofing that covers 100 square feet or an area that measures 10' by 10'. If we are able to calculate total roof area, we can find the number of squares of roofing needed simply by multiplying the total area by the unity fraction: 1 SQUARE 100 ft 2

3. Roof Slope The roof slope symbol is the symbol placed on a profile view of the roof which shows roof slope in relation to its rise and run. The rise is always given in relation to a run of 12 units. The symbol below represents a 4/12 slope, the rise being 4 units and the run being 12 units. This means that the line that is drawn to represent the roof rises 4 units for every 12 units that is travels horizontally.

4. Rafter The rafter is that structural roof member that extends from the ridge board to the fascia board. Looking perpendicular to the side of a gable roof it represents the width of the rectangle that is formed by the roof surface on that side of the house. It, therefore will be used, along with the roof length, to calculate roof area. By using the Pythagorean theorem we can figure out the rafter length.

5. Pythagorean Theorem The Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. Where c represents the hypotenuse and a and b represent the other two sides, the equation would read c = a + b This equation coupled with the roof slope symbol and the theory of similar triangles can be used to find rafter length. 222

6. Theory of Similar Triangles The theory of similar triangles states that if, in two triangles, the corresponding angles are equal then the ratio of corresponding sides are proportional. In the similar triangles below a/b = A/B similarly c/a = C/A. The ratios of any other combination of corresponding sides would also e equal. =

7. Building Dimensions Looking at the figure below we can see a roof slope triangle showing a slope of 4/12. We can see a building width of 30'-0”. When we add the two 2'-0” overhangs to the building width, we can see that the total distance between fascia boards is 34'-0”. We can also see that the length of the roof is equal to the building length of 65'-0” plus the two 1'-0” overhangs for a total roof length of 67'-0”.

8. Step 1

9. Step 2 Lets now compare the roof slope triangle to the triangle formed by the roof rafter and its rise and run. We know the roof rafter run to be half of the total distance between fascia boards (which we previously determined to be 34'-0”). One half of 34' is 17'. Comparing the rafter triangle formed by the rafter and its rise and run, and the roof slope triangle we have the two figures below. We've labeled the hypotenuse of the rafter triangle “WIDTH” since it represents the width of the rectangular shape of the roof surface.

10. Step 3 Substituting into the theory of similar triangles we can see that, from the slope triangle, the ratio of hypotenuse to base or 12.65/12 is equal to, the hypotenuse of the rafter triangle over its base or WIDTH/17'. Setting this up in ratio proportion form: 12.65 12 WIDTH 17' =

11. Step 4 12.65 12 WIDTH 17' = Solving for WIDTH by multiplying both sides of the equation by 17' and canceling where possible we arrive at the equation. 12.65 12 WIDTH 17' = ( )‏ =17.92' ( )‏

12. Step 5 The 17.92' just calculated, is the rafter length and is also the width of the rectangular roof surface on one side of the gable roof. 12.65 12 WIDTH 17' = ( )‏ =17.92' ( )‏

13. Step 6 A=LW=A=(67')(17.92')=A=1200.6ft Substituting the WIDTH value of 17.92' and the length of the roof, previously determined to the 67', into the area equation we arrive at the equation” Since the gable roof has two sides we multiply 1200.62 ft x 2 to arrive at a total roof area of 2401.2 ft. 2 2 2

14. Step 7 To determine the number of squares of roofing needed to cover the roof we multiply our total roof area by the unity fraction 1 SQUARE/100 ft. Our total number of squares = 2401.2 ft 2 2 2401.2 ft 1 SQUARE 100 ft x 2 2 THE NUMBER OF SQUARES == 24.01 SQUARES