Area Larger Than Perimeter?

Date: 04/15/2002 at 20:14:13
From: Daniel
Subject: Area and perimeter

Can the area of a shape be larger than the perimeter?

Date: 04/15/2002 at 23:11:40
From: Doctor Ian
Subject: Re: Area and perimeter

Hi Daniel,

Strictly speaking, they're not comparable.  It's sort of like asking 
whether a second is larger than an inch. 

Think about it this way.  Suppose I have a square that is 1 foot on 
each side:

       1 ft
    +-------+
    |       |
    |       | 1 ft
    |       |
    +-------+

The area is 1 square foot; and the perimeter is 4 feet. So you'd think 
that the perimeter is bigger, right?  

But here is the same square, measured in different units:

      12 in
    +-------+
    |       |
    |       | 12 in
    |       |
    +-------+

Now the area is 144 square inches, and the perimeter is 48 inches. So 
you'd think that the area is bigger, right?

But you'd think that one is larger or smaller than the other only if 
you look at the numbers and ignore the units. When you look at the 
units, you see that the quantities can't really be compared, so the 
question of which is 'bigger' doesn't really make sense. 

Does this help? 

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