Calculating the number of tiles needed for a roof
The Sunday Nation
Nairobi,
29 May 2022
Francis Obare sent me
an “urgent request for help”. He says he is building a “simple house”
and is about to start roofing. His builder (fundi) worked out the
number of roofing tiles needed and Francis says he is doubting the
calculation.
“It is a simple
rectangular structure measuring 5.5m by 8m [on which] we are putting
small iron sheet tiles of 1.5m by 0.5m in size. When I divide the area
of the house by the area of the tiles, I get 58.7 tiles. So, I think if
I buy 60, they should be enough.
“But the fundi
insists that I should buy 95 tiles. I am not convinced. That number
appears too high. Is my fundi cheating me or is there something
that I am missing?”
There was a crucial
piece of information missing from this message: the gradient of the
roof. The steeper it is, the more roofing material it will require. So,
I asked Francis to check what was indicated in the blue-prints. The
answer was 30 degrees.
It is easy to
visualise that the length along the slope of the roof is longer than the
horizontal measurement taken on the floor. The 5.5m by 8m that Francis
is referring to are taken horizontally. So, this area (44 square metres)
is smaller than that of the sloping roof. The question is: by how much?
To get the answer, we
must go back to secondary school mathematics of right-angled triangles.
No! Not Pythagoras theorem! Sines, cosines and tangents: the ratios of
the sides of such a triangle.
In Francis’ problem,
we know the angle between the horizontal floor and the sloping roof (30
degrees). We also know the horizontal area (5.5m by 8m = 44sq.m.). So,
the trigonometric ratio we shall use is the cosine; Thus, the cosine of
30 degrees is equal to the horizontal area divided by the sloping roof
area.
From my calculator,
cosine of 30 degrees is 0.866; thus, area of the sloping roof is
44/0.866 = 50.8sq.m. Therefore, Francis needs 50.6/0.75 tiles; that is,
67.7, or 68 tiles.
Now this is still
quite far from the 90 the fundi is asking for. My guess is that
we have not factored the eaves around the house. These are usually about
half a metre wide, meaning that the actual covered space is 6.5m by 9m.
Repeating the calculation with these new measurements yields 91 tiles.
This is a better estimate and I conclude that the fundi has done
his math correctly.
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