Calculating Square Footage or Area

Date: 01/08/2007 at 07:34:47
From: Melissa
Subject: square footage

I recently got a job at a home improvement store, and I am constantly
asked to figure out square footage.  I need the formula that is used
on most areas like square and rectangle.  Also, what if a wall is not
square like a triangle or odd shape.

Date: 01/08/2007 at 16:05:27
From: Doctor Peterson
Subject: Re: square footage

Hi, Melissa.

The basic formulas are:

  Rectangle: A = lw      (area = length times width)

  Triangle:  A = bh/2    (area = base times height divided by 2)

The triangle formula really means that the area of any triangle is 1/2
that of a rectangle with the same base and height:

  +----+--------------+
  |   /...\           |
  |  /.......\        |h
  | /...........\     |
  |/...............\  |
  +-------------------+
            b

With these two formulas, which are really almost just one formula, you
can find the area of any region with straight edges, by breaking it up
into rectangles and triangles.  For example, suppose you had to find
the area of this shape:

                 12
  +-------------------------------+
  |                               |
  |                               |3
  |                               |
  |                 +-------------+
  |                 |      5
  |                 |
11|                 |4
  |                 |
  |                 +
  |              /
  |           /
  |        /
  |     /
  |  /
  +

You can break it up several ways.  Here is one:

                 12
  +-----------------+-------------+
  |                 |             |
  |                 |      A      |3
  |                 |             |
  |        B        +-------------+
  |                 |      5
  |                 |
11|                 |4
  |                 |
  +-----------------+
  |              /
  |   C       /
  |        /
  |     /
  |  /
  +

We have to find the length and width of each piece.  Since the width
of piece A is 5, it uses up 5 feet of the top edge, leaving 12-5 = 7
feet for piece B's width.  Similarly, piece A is 3 feet high, so the
total height of piece B is 3+4 = 7 feet.  That means that piece B is a
square 7 by 7 feet.

How about piece C?  Its width is the same as B (7 feet); and since
B's height of 7 feet uses up 7 of the 11 feet of the total height, C's
height is 11-7 = 4 feet.  That means the base of C is 7 feet, and its
height is 4 feet.

           7               5
  +-----------------+-------------+
  |                 |             |
  |                 |3     A      |3
  |                 |             |
  |7       B        +-------------+
  |                 |      5
  |                 |
  |                 |4
  |       7         |
  +-----------------+
  |              /
  |   C       /
  |4       /
  |     /
  |  /
  +

The area, then, is

  Area = Area A + Area B + Area C
       =   3*5  +  7*7   + 7*4/2
       =    15  +   49   +  14
       = 78 square feet

If you ever have to measure anything round, you'll need the formulas
for a circle, but that's probably not common in your everyday work.
Let me know if you'd like them.

I'd recommend that you look in your library or bookstore for a review
book on basic geometry or practical math that has a chapter on this
sort of problem.  Doing a few exercises after looking through how they
demonstrate it in the book will probably help a lot.  It's a lot
easier to learn something like this when you have a reason (such as
being paid for doing it!) than it probably was in school.

If you have any further questions, feel free to write back.


- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/