Area of an L

Date: 07/10/2003 at 23:15:40
From: Heather
Subject: Area

How do you find the area of an 'L' shaped object?

I know that area is LxW, but with the irregular shape of the 'L', I 
am not sure how to work the problem. Could it be that you cut the top 
off the 'L' and find that area, then add it to the bottom part of the 
'L' which you also find separately?

Date: 07/10/2003 at 23:35:48
From: Doctor Peterson
Subject: Re: Area

Hi, Heather.

You can either cut the area up into non-overlapping rectangles and 
add their areas, or think of the L as a large rectangle minus a 
smaller rectangle:

      a                  a
    +---+              +---+-----+
    |   |              |   |     |
    |   |c             |   |c    |
    |   |  b        c+d|   |  b  |
    +---+-----+        |   +-----+
    |         |d       |         |d
    +---------+        +---------+
        a+b                a+b

  A = ac + (a+b)d   A = (a+b)(c+d) - bc

These give the same answer. In fact, there are several other ways you 
could do it and still get it right!

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

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