Lesson 2 of 13
Area, Perimeter and Volume
This is the lesson that decides what you order and what you pay for. Get it right and the truck brings the right amount. Get it wrong and you are either short at four in the afternoon or eating the difference.
Step one
Read the material
Three ideas, and the first one does most of the work.
Concept one
Break the odd shape into shapes you can compute
Almost no room is a clean rectangle. There is a bump-out, a closet, a chimney chase, a stair opening. You do not need a formula for an L-shaped room, because there is no such formula worth carrying.
Instead, cut the shape into rectangles with a pencil line, compute each one, and add. Or take the whole rectangle it would be if the notch were filled, compute that, and subtract the notch. Both roads land on the same number, and the second is usually fewer steps.
Perimeter is different and simpler: it is just the distance around the outside, and on an L-shaped room it comes out the same as the rectangle it sits inside. That surprises people, and it is worth checking once on paper so you believe it.
Concept two
Triangles and circles
A triangle is half of the rectangle that would box it in: base times height, divided by two. That is the gable end, the corner of a hip roof, the odd cut at the end of a run of flooring.
A circle is pi times the radius squared, and the mistake is using the diameter where the radius belongs. Halve the diameter first, every single time. For a round column footing, an area in square feet times the depth in feet gives you the volume, and then you are into the third idea.
Concept three
Volume, and the cubic yard
Volume is area times thickness, in the same units. The trap is that slab thickness is spoken in inches while everything else is in feet, so convert the thickness first: four inches is four twelfths, which is 0.333 feet.
Concrete is sold by the cubic yard, and a cubic yard is twenty-seven cubic feet, because three by three by three is twenty-seven. So compute cubic feet, then divide by twenty-seven.
A twenty by thirty slab at four inches is 600 square feet times 0.333, which is 200 cubic feet, divided by 27, which is 7.4 yards. Order eight. Nobody was ever fired for having a quarter yard left over, and everybody remembers the pour that came up short.
Step two
Work it with your hands on it
An L-shaped room. Set the overall size and the notch, and watch it split into two rectangles you can actually compute. Then give it a thickness and it becomes a pour.
Hands on it, off the screen. Take a tape to a room in your own house that is not a plain rectangle. Sketch it, cut it into rectangles with a pencil line, measure each piece, and total it.
Then measure the outside distance around the room and compare it to the perimeter of the rectangle it sits inside. See for yourself whether they match.
Step three
Prove you understood it
One question per idea, new numbers every time.
All three solid.
You can take an odd room apart into shapes you can compute, handle a triangle and a circle, and turn a slab into cubic yards. Lesson three is the triangle that runs under the rest of the class.
Trades Geometry
Lesson two of thirteen. Written by our founder, Dr. Gene A Constant, and donated to the Foundation. Published by Global Sovereign University Press.
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