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You can't really compare perimeter and area.
Perimeter is a linear measure, area is a two-dimensional measure. They are not directly comparable.
You get strange results if you do.
Lets say the radius of a circle is 3 cm.
The perimeter is 6pi cm
The area 9pi cm2
But 3 cm is exactly the same thing as .03 m.
So if we use .03 m instead, we get:
The perimeter is .06pi m.
The area is .0009 m2.
If we try to just compare the numbers without taking the units into account, we see that for exactly the same circle in the first case the area is a larger number, in the second case the are is a smaller number.
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Can you calculate the area if you know the perimeter?
No, you can not calculate an area if you know just the perimeter. For example, rectangle with sides of 10 and 20 would have a perimeter of 60 and an area of 200, but a square of sides 15 would have a perimeter of 60 and an area of 225. You need to know more details about the shape than just the perimeter.
Is the perimeter of a polygon less than the area of the polygon?
if your perimeter totals the same as 4 times pi then the maximum area that can be encompassed is equal to the perimeter. This is done by forming a circle. if you change the shape of the circle then the area will become smaller than the perimeter(circumference) if you make the circumference of the circle smaller then you will definitely decrease the area faster than you would the perimeter if you make the perimeter bigger then you will definitely increase the area faster than you would the perimeter.
Can a rectangle have a greater perimeter and also have a greater area?
Of course, a rectangle can have a greater perimeter and a greater area. Simply double all the sides: the perimeter is doubled and the area is quadrupled - both bigger than they were.
Can a rectangle have a greater perimeter than another one but have a greater area too?
yes it can; a rectangle 5 by 2 has perimeter 14 and area 10 for example; a rectangle 10 by 2 has perimeter 24 and area 20, both greater.
Can perimeter be larger than area?
yes if you have a 1 by 1 rectangle, you would have a perimeter of 4 but an area of 1 [ADDED} It's really a meaningless question because although such numbers suggest that, you cannot compare a linear dimension (perimeter) with an area.
