Calculating the area of rectangles

- Let's apply what we've discussed about area by taking a look at the floor plan for a typical office building. We see lots of shapes, let's zoom in to one that's a simple rectangle and apply our newly learned skill of calculating the area of a rectangle room and then combine it with what we discussed earlier regarding converting units. Whether you measure the room on this set of plans or measure it with a tape measure out in the field, you should get a length of seven foot 6 3/4 inches and a width of 19 feet 8 3/4 inches. Written using fractions, that math problem looks like this. All of a sudden, our simple length times width calculation looks a little more complicated. I'm pretty good at math and I can calculate this, sticking with the fractions and all. But that's really going to slow me down. On the other hand, I also don't want to just round up to the nearest foot and turn the problem into eight feet by 20 feet. I want my calculations to be precise. If I want to add a waste factor when I'm ordering materials, I'll do that separately. So let's figure out the area of this room by converting the measurements before we run the calculations. And I'll show you two different ways to go about this. The challenge here is that our measurements consist of feet and inches and they include fractions. I want to change this so I'm dealing with a single unit and I want to deal with decimals instead of fractions so I can just plug this math problem into a calculator and get an answer. Option one is to convert the measurements to inches. First, let's convert those fractions to decimals, though, making the length seven foot 6.75 inches and the width 19 feet 8.75 inches. Next, let's convert feet to inches. Seven feet becomes 84 inches and I have to add that to that remaining 6.75 inches to give us a total length of 90.75 inches. Doing the same thing to the width converts 19 feet to 228 inches plus that remaining 8.75 inches means the width of this room is 236.75 inches. Now I have a math problem that I can easily enter into any calculator to get the answer. Just multiply 90.75 inches times 236.75 inches for an answer of 21,485.0625 square inches. Last, let's convert this answer back to square feet because the boss asked us how many square feet this room is. Looking back on our cheat sheet I gave you earlier in the course, I see that there are 144 square inches in one square foot. If I divide that 21,485.0625 square inches by 144 square inches per square foot, I get a numerical answer of 149.2 and if I'm paying attention to my units, dividing square inches by square inches cancels those units out and leaves us with square feet meaning we now have an answer of 149.2 square feet. Let's take a look at option number two which is to just convert those inches to feet and then run the math. So 6 3/4 inches or 6.75 inches converts to .5625 feet making the total length of the room 7.5625 feet. 8 3/4 inches or 8.75 converts to .7292 feet making the total width of the room 19.7292 feet. Again, now that the units are the same, I can just enter 7.5625 feet times 19.7292 feet into a calculator and get an answer of 149.2 square feet. There's two different approaches to arrive at the same answer and you can start to see why you need to understand the units involved even when you're using a calculator to calculate something as simple as the area of a rectangle. One last thing before we move on, since this is construction math, let's talk about rounding numbers. I started this discussion earlier in the course when I discussed measurements. When you're reporting measurements, you need to decide how to round off your numbers. Now I'll discuss that throughout this course but in this particular example, if I'm talking to somebody about the square footage of this room because I'm ordering flooring material, I would want to round up and say this room is 150 square feet. If I round down and say it's 149 square feet, I'm actually reporting a number that's less than the actual calculated area meaning I could end up short on material.