Math and Geometry for roofs

1. ROOF GEOMETRY
GABLE ROOF
SIMILAR TRIANGLES
PYTHAGOREAN THEOREM

2. ISOSCELES TRIANGLE
2 sides equal

3. The Perpendicular Bisector divides the base into 2 parts.

4. Two Equal Triangles  Equal Angles

5. THIS IS THE LINE DRAWING OF THE SIDE VIEW OF THE GABLE ROOF
AB = AC = Rafter line; BD = DC = Total Run; BC = Total Span; AD = Total Rise

6. 𝐴2 + 𝐵2 = 𝐶2
C = (𝐴2 + 𝐵2)
Video on Pythagoras' Theorem
http://learni.st/learnings/99012-pythagoras-theorem?board_id=13622

7. This is a D.A.L. calculator
• Direct Algebraic Logic
• You enter numbers and symbols
as you would write them
PYTHAGORAS’ THEOREM
Given: A = 4’, B = 3’
Find: C
Calc.: C = (𝐴2 + 𝐵2)
On the Calculator:
Press: ( 4 x2 + 3 x2
Screen: (42 + 32) = 5

9. Roof Slope is denoted by the # of inches of rise over
12” of run.
i.e. vertical rise over the unit horizontal run of 12”
Slope(imp.) =
(𝑈𝑛𝑖𝑡 𝑅𝑖𝑠𝑒)"
(𝑈𝑛𝑖𝑡 𝑅𝑢𝑛)"
=
(𝑈𝑛𝑖𝑡 𝑅𝑖𝑠𝑒)"
12"
=
6
12
, for example
Written as 6 in 12, 6:12, 6/12, or
6
12
In metric, as per the Building Code,  1 in 2 or 1:2
12
6
12
6

10. Pythagorean Theorem
6
12
Hypotenuse
Hypotenuse = (62 + 122)
= 36 + 144
= 180
= 13.42”
This is called the unit length
of the Common Rafter.