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PMarch 18, 2011

# My Short Geometry Lesson

Did you know that the exterior wall construction in a building could represent more then 20% of the total cost of the building? And did you know our estimating department performs an exterior wall assembly analysis to determine if the ratio of exterior wall to building square footage is within our cost parameters? This is very helpful especially if the ratio is off the charts!

So what is the ratio of the total area of the exterior wall as it relates to the total square feet of the building? Before we can attempt to answer that question we will need a short refresher course on geometry…. keyword is short! The most efficient ratio of an area and the linear feet (LF) of what makes up that area is a circle. Please note this is for illustration purposes only, not an endorsement on cornerless buildings!

Let’s assume the circle shown is 10,000 sf. Do you remember the formula for an area of a circle? Πr2 Pi is easy…3.14 so if the area is 10,000 sf divide 10,000 sf by pi = 3,185 then do a square root calculation for the “R”adius√3,185 =56.44 so now we have the radius…56.44.

Now on to circumference…2Πr 2 x 3.14 x 56.44= 354.44 LF, a ratio sf to LF of .035 or .035 x 10,000 sf = 354LF

The second most efficient geometric shape is a square. Lets still assume a 10,000 sf square or an area that is 100 x 100 with a total LF of 400 or a ratio of .04.

Now let’s move on to our architectural gem. The area is still 10,000 sf but the LF of exterior wall is 610 LF or a ratio of .061… an incredible 74% more then the perfect circle and just as astounding, an increase of 53% over a square.

If we apply this mathematical exercise and in the vernacular of estimators…”Put a pencil to it” we get the following answers:

Area: 10,000 sf

LF wall: 610

Ratio: .061

Wall Area 9,150 sf

Cost of exterior wall: 9,150 sf x \$44.00 sf = \$402,600

Cost of Building: \$1,400,000 or \$140.00 sf

Percentage of cost: 28.75%

If we are able to remove 18% of the exterior wall in our architectural gem (a mere 109LF) we are able to save almost \$72,000 without changing anything inside the building and still maintain more then a 100LF more then a boring square!

Our estimators are always looking for easy ways to save money and our exterior wall analysis adds one more tool in their electronic toolbox. 