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Logo Area

Date: 03/26/2003 at 21:06:37
From: Cheyenne
Subject: Finding the area in square units

How do we find the area in square units following the Logo command?

Logo command
fd 40 rt 90 fd20


Date: 03/26/2003 at 23:28:07
From: Doctor Ian
Subject: Re: Finding the area in square units

Hi Cheyenne,

Let's simulate what the turtle would do to find out. Let's assume it
starts out facing to the right:

  O>

We tell it to go forward 40 units:

            40
  . . . . . . . . . . O>
                      

then turn right 90 degrees, 

            40
  . . . . . . . . . . O
                      v

then go forward 20 units, 

            40
  . . . . . . . . . . .
                      .
                      . 
                      . 20
                      .
                      O
                      v

Now, in one sense, there's no 'area' yet, because the turtle hasn't 
yet returned to the starting point. Does that make sense? But it 
_might_ go back to complete a rectangle:

  ^         40
  O . . . . . . . . . .
  .                   .
  .                   . 
  .                   . 20
  .                   .
  . . . . . . . . . . .

In this case, the area would be the width times the height, 

   area(rectangle) = width * height

                   = 40 * 20

                   = 800

But it might go straight back, to complete a triangle:

  ^         40
  O . . . . . . . . . .
      .               .
          .           . 
              .       . 20
                  .   .
                      .

In this case, the area would be half the area of the rectangle,

   area(triangle) = (1/2) * base * height
 
                  = (1/2) * 40 * 20

                  = 400

Or it might wander all over the place!

  ^         40
  O . . . . . . . . . .
    .                 .
     .                . 
      .        .      . 20
       .     . .      .
        .  .   .      .
         .     .   .
               . .
               .


Do you see why you need to know how the turtle gets back to where it
started before you can figure out the area? 

If you're not completely comfortable with the idea of area yet, you
might want to take a look at this:

   Area and Perimeter
   http://mathforum.org/library/drmath/view/57652.html 

Does this help? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/ 
Associated Topics:
Elementary Geometry
Elementary Triangles and Other Polygons

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