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### The Relation of Perimeter to Area

```
Date: 10/2/95 at 14:57:55
From: Kurt S Merz
Subject: ?????

I'm puzzled by the ability of two fences to have the same
perimeter with very different areas inside them. I realize by LxW
an 8' x 10' fence will have more area than a 6' x 12' fence, but
WHY?  Both fences  have 18' surrounding them but different areas.
Also does a circle or a  square conserve more area with identical
perimeters?  Thanks for your time.

Shawn
```

```
Date: 10/7/95 at 2:33:5
From: Doctor Andrew
Subject: Re: ?????

I confess that your question has stumped me for a good answer.
Often I've wondered why this is true.  I think it is easier to see
with a stranger shape than a rectangle.  Imagine that instead of a
rectangle with straight sides you made the sides all squiggly.
The rectangle would still have about the same area but the
perimeter would be much longer than for a simple rectangle.  So we
can see that perimeter really doesn't need to be related to area
at all.  In fact, there are shapes called fractals that have only
a small amount of area and an infinite perimeter (that means that
no length of string could follow the edge of the shape; pretty
strange).

>Also does a circle or a square conserve more area with identical
>perimeters?  Thanks for your Time.

A circle holds more area compared to its perimeter than any other
shape.

I hope this helps.  Please send us any more questions you have.

-Doctor Andrew,  The Geometry Forum

```
Associated Topics:
Middle School Conic Sections/Circles
Middle School Geometry
Middle School Triangles and Other Polygons
Middle School Two-Dimensional Geometry

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