I've been wanting to do this topic but couldn't come up with the easiest way to teach it; while it is possible to measure the quantities of roofing sheets needed for your project even before you set the first block using the Architectural drawings; it requires a lot of experience especially in trigonometry and site visualization. I have however found an easy way around it; as would be discussed below.
I have carefully designed and attached a roof plan for this purpose, (feel free to use should it fit your building design... lol)
Calculating the quantity of roofing sheet needed is done is meter square (m2), same parameters used for selling and purchasing roofing sheets hence we would expect to use the AREA FORMULAS (i.e Area formulas for Rectangle / Square, Triangle, Trapezium and Rhombus), sounds easy right? Yes it is!!!
The most difficult aspect of calculating Area of Roofing is FINDING THE TRUE LENGTH (Technical Drawing students should understand this) and that is infact why I opted for the practical way to calculate because I expect the roofing carcass to have been done on site before you can apply this teaching by asking your carpenter to measure key length as we would explain soon. (We would also discuss finding TRUE LENGTH in brief at the end of this tutorial)
LETS GET TO BUSINESS....
Diagram 1: shows the roof plan and the front elevation of a building while
Diagram 2: shows the division and label to guide us in our calculation.
Diagram 3: shows the dimensions of lengths that are ALREADY IN THEIR TRUE LENGTHS (those not labeled would have to be measured on site or calculated)
We would calculate the roof per section eg R1, R2, etc and add up later. (PRINT OUT THE ATTACHED DIAGRAMS)
Let's start by calculating R1.
The shape R1 is a triangle, so we would use the triangle formula (½BxH) where B = (A+B) in Diagram 2 = 9m and H is the true length of C. (ask your carpenter to measure (A+B) and C on site and write down the distance in meters). Measuring from my drawings C = 6.15m
Hence area of R1 = (9m x 6.15m) / 2
Area of R1 = 27.68m² (what this means is that minus waste, we need 27.68m² of roofing sheet to roof R1 alone) we would add waste after the entire exercise.
Now let's calculate R2:
The shape R2 is a trapezium hence the formula would be ½x(A+B)xH - (notice i divided R2' out) here the carpenter should measure the following distances and you can note them down; R, (F-K) and D in true length. R = 7m, F-K = 18.4-2.4 = 16m and D = 6.15m (measured from my drawings).
Hence area of R2 = ½ (7+16) x 6.15 = (23m x 6.15m) / 2
Area of R2 = 70.73m²
I separated R2' to make the calculation and formula application simplier. R2' wld now be calculated as a Rhombus using formula L x B.
Hence area of R2 = O x O' = 2.4m x 3.05m (measured from my drawings as I expect you to measure from site)
Area of R2' = 7.32m² also note that R2' = R7 hence R7 = 7.32m²
LETS FAST TRACK THE CALCULATIONS
R3 = R2 - (the small triangle in R4&R5) so I'll calculate the small triangle and subtract from R2.
hence; the area of the smaller triangle using same principle from R1 = (7m x 4.7m ) /2 = 16.45m²
R3 = 70.73 - 16.45 = 54.28m²
Now let's calculate R4 & R5: The trapezium formula applies here also; measure F, I and Q where F is the true length and F = H in the formula ½x(A+B)xH
= ½ (3.99+7.49) x 4.8 = (11.48m x 4.8m) / 2
Area of R4 = 27.55m²
Area of R5 = 27.55m² also
Now let's calculate R6 and R8: If you look at the roof plan critically, you would notice that R6 + R8 = A perfect Triangle; so instead of calculating them separately, draft it into a complete triangle and calculate using the triangle formula. Coincidentally also, R6 +R8 = R1 so lets just pick the figures from R1.
Hence R6+R8 = R1
Area of R6+R8 = 27.68m²
TOTAL AREA OF ROOFING SHEETS NEEDED THEREFORE = R1+R2+R3+R4+R5+R6+R7+R8
= 27.68 + 70.73 + 7.32 + 7.32 + 54.28 + 27.55 + 27.55 + 27.68
Now lets add waste of 10% - 20% depending on the roofing material e.g. Gerard roofing sheet would generate more waste than Long Span roofing sheet.
ADD 20% = 250.11 + 20% of 250.11 = 250.11m² + 50.02m²
TOTAL AREA OF ROOFING SHEETS = 300.13m²
Multiple 300.13 by the price of 1m² of roofing sheet eg N3200 (Gerard) = 300.13 x 3200 = N960,416:00k (Minus Accessories)
I'll briefly explain calculating TRUE LENGTH of C in R1 below.
HOW TO CALCULATE THE TRUE LENGTH OF C IN R1 (diagram 1,2,3 above) also see attached diagram below
From the Architectural Drawings you can get the HEIGHT AND BREATH OF THE ROOF, what the drawings won't tell you is C (I dimensioned it thou for learning purpose in the attached diagram)
USING TRIGONOMETRY A² + B² = C²
= 4.2² + 4.5² = C²
= 17.64 + 20.25 = C²
C² = 37.89
C = Root of 37.89
C = 6.15548
C = 6.155 (same with the dimension from AutoCAD)