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
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