Additional Math Pages & Resources

Thursday, March 24, 2011

Square Footed, Part II

This blog is about how grown-ups use math they learned as kids. Hopefully you learned with our Excel Math curriculum.

Yesterday we talked about square footage of a house, calculated from its floor plan. We calculated the size of a house's footprint. Today we look at another way to indicate the size of a house. This could be called its hat size.

The area of a roof is usually larger than the square footage of the floor plan under the roof.  The roof protects the house from falling rain and snow, so it should be larger than the area it is protecting. How much larger? It depends. The local weather, neighborhood styles and the architects determine the roof design.

A multi-story house might have a smaller roof area than floor area because there can be several floors whose areas are added together.

Here is our sample house from yesterday, covered with a roof of my choosing. First, a transparent version to show that all rooms are covered. From this drawing you cannot see the slope of the roof (how high the peaks are), but I put in a few gables (sub-roofs) for variety.

I also made a more detailed drawing below, to show how I might calculate the roof's area (there are other ways you could do it):

NOTE: The dimensions will have to come from the architect and not from this drawing, because it does not portray a flat surface like a floor.
  1. Find the yellow roof area R by multiplying the length and width of RA and RB and adding them together. 
  2. Calculate the area of Chimney X and subtract it from R.
  3. Now find the area of the gables. Multiply L x W for each section of the roof. For the area of a right triangle (AE and AF), the formula is (L x W) ÷ 2. The triangular regions are shown in green.
  4. Gable A's area is the sum of the areas of AA + AB + AC + AD + AE + AF. Use the same process for the other gables.
  5. Now subtract from R the area covered by gables above R. We only need to know the areas covered by the green and blue sections.  (I calculate the purple areas separately because they add to R and do not overlap it.)
  6. We won't do the exact overlap calculations here because it's a complex job to accurately calculate the slices of a sloping roof section.
  7. So the complete process is: Get roof area R, learn area of gables A, B and C and add these all together. Subtract the overlapped areas of R shown in blue and green.

The result is the hat size, or area of the roof in square units. Now that we have done all this work, it's time for me to tell you that roofers in many English-speaking countries use their own unit of roofing measure, called a square (100 square feet of material). They use special terms too, such as hips, valleys, peaks, ridges, eaves and rakes and pitch.

My 2200 square foot house needed 30 squares of material. That's about 3000 sq ft of roof.

Here are a couple sites that can help you measure your own roof, or you could special calculator device, or a roofing calculator app for your phone.



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