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/ |
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