Perimeter and area - need explanation

[PeteCA]

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 ?

 

[Number Nine]

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.

 

[PeteCA]

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.

 

[Number Nine]

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.

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.

 

[CellCoree]

The reason why the area of the circle is not the same as the area of the rectangle is because they are two different shapes with different formulas for calculating their areas. The area of a rectangle is calculated by multiplying its length (a) by its width (b), while the area of a circle is calculated by multiplying the square of its radius (r) by pi. In this case, the rectangle has an area of 10 square meters, while the circle has an area of 15.597 square meters. This is because the circle has a larger radius (2.228 meters) compared to the width of the rectangle (2 meters). It is important to remember that even though the perimeter may be the same, the area will be different for different shapes.