As an engineer, numbers must make sense, so roofing should be no exception.
A roofing contractor came over to give an estimate. To simply things, lets assume that the front of the house is 46 feet wide and the side is 30 feet wide. The pitch of the roof is 7/12 (7 feet up for every 12 feet of Horizontal run) and is a simple 'A' type roof. So far so good. Now for fun part. The estimator used the following equation:
((Side of House * Front of House) * (1 + Pitch))*(Waste)/100 = # of Squares.
Filling in the values
((30' * 46') * (1 + 7/12))*(1.1)/100 = # of Squares. = ~24.03 Squares
where a square is 100 Ft^2 and a waste factor of 10% or 1.1 multiplier.
Now for the Engineering Math that is based of the principles that the side of the house is 2 right triangles and the right triangle theorem of A^2+B^2=C^2
=(((Side of House/2*(Pitch))^2+(Side of House/2)^2)^0.5*Front of House)*2*Waste/100
Filling in the values:
=(((30/2*(7/12))^2+(30/2)^2)^0.5*46)*2*1.1/100 = 17.57 Squares.
To double check the above equation, half of the side of the house is 15', the rise over 15 feet with a 7/12 pitch would be 8.75' Therefore the 'C' part of A^2+B^2=C^2 is 17.365 feet.
Then to determine the area of half of the roof is 17.365' * 46 = 798.8' So double it and then multiply by the waste factor of 1.1 results in 1757 ft^2 or 17.57 squares.
All this to show that 'engineering math' results in 17.57 squares and 'contractor math' is ~24 squares.
OK now for the question. Who's math is correct and what is the standard for determining the # of squares when the roof top is not measured and only horizontal numbers are used???
Thanks,
