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The fence and the field

How Are Area and Perimeter Different?

Perimeter measures the walk around the edge; area measures the space inside.

Perimeter The fence around thefieldArea The grass inside it
One is the fence. The other is the field.
  1. Step 1 of 5

    Perimeter is simply the walk around the edge.

    1 Start at acorner2 Follow everyside3=Add the sidestogether

    Set off at one corner, follow every side back to where you started, and add up the distance. That total is the perimeter.

  2. Step 2 of 5

    It is a length, so the units are plain.

    Perimeter — metresa distancewalkedArea — square metressquares covered

    You are measuring a distance, so the answer is in metres, not square metres. Nothing is being covered, only walked along.

  3. Step 3 of 5

    Same perimeter, wildly different areas.

    Both need 16 mof fenceOne holds 15square metresThe other only7

    A long thin rectangle and a near-square can need identical fencing yet hold very different amounts of space inside them.

  4. Step 4 of 5

    The squarer the shape, the more it holds.

    1 m by 7 mlong and thin2 m by 6 mgetting squarer4 m by 4 ma square, thebest

    For a fixed amount of fence, area grows as the shape gets closer to square, and a circle does better still than any rectangle.

  5. Step 5 of 5

    Which one matters depends on the job.

    Buying fence Perimeter decides thecostBuying turf Area decides the cost

    Fencing a field, framing a picture or edging a lawn are perimeter jobs. Turf, paint and carpet are area jobs.

    Of all shapes with the same perimeter, a circle encloses the most area — which is why bubbles and pipes are round.

The short version

One is a length in plain metres, the other a count of squares — and the same fence can enclose wildly different amounts of field, because area grows as the shape squares up, with a circle beating every rectangle there is.

Try it yourself

Make a 16-piece loop of string into a long thin rectangle, then a square. Same string, but the square clearly holds more space.

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