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Perimeter and area - need explanation

  1. Oct 10, 2011 #1
    Dimensions of rectangle are a=2 and b=5.

    Perimeter and area P=2a+2b=14 and A=a*b=10

    If we take a rope of length l=14m, encircle the rectangle and connect the ends we will have the same perimeter.

    Now we take this rope and make circle of it, this circle will have the same perimeter of rectangle P=14.

    Radius is r=(14)/(2*pi)= 2.228

    Area of circle will be A=r*r*pi=2.228*2.228*pi=15.597

    Why area of circle A=15.597 is not the same as area of rectangle A=10 ?
     
  2. jcsd
  3. Oct 10, 2011 #2
    Because area is not the same as perimeter. Take that circle of yours and crush it flat (well, almost; you can't really crush it into a line...); it now has ~zero area and the same perimeter. Incidentally, it's possible for a figure to have finite volume and an infinite perimeter.
     
  4. Oct 10, 2011 #3
    Then why is land mesured in area and not perimeter, every mesure will give different results.

    Is there a formula or easy way to mesure land if boundaries are like potato.
     
    Last edited: Oct 10, 2011
  5. Oct 10, 2011 #4
    Because no one cares what the perimeter is, and no one wants to end up buying property with zero square feet because some sales rep was clever in advertising the place.
     
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