If peripheral length of any two geometric shapes is same will their area same?

Answer 1

No:
Rectangle 10x2 has PL=24, A=20, but square 6x6 has PL=24 and L=36.

Answer 2

Dr D has the right idea. Imagine that you have a partially filled soft plastic bottle with no air gap, so that it's somewhat crumpled. You will find that it's not hard to deform that plastic bottle into other shapes, even though it contains the same amount of liquid and has the same surface area. Only when the bottle is filled to maximum capacity that it becomes hard to deform. A circle, for example, as a shape of fixed perimeter and area, cannot be deformed (because the circle has the maximum possible area for a given perimeter), but an oval of fixed perimeter and area can be (because an oval does NOT have the maximum possible area for a given perimeter--i.e., other oval-like shapes have same perimeter and area). I've given this question a star because as simple as this question is, it does have significance in structural mechanics, such as in design of spacecraft. Addendum: Expanding on Zanti3's answer, think of any geometric shape, with a "hole" inside of it, also of any gemoetric shape. Obviously the total perimeter and total area are both constant, but the hole can be moved anywhere inside.

Answer 3

The answer is no.
Fold a piece of string in half and tie a knot near the loose ends..Open it up to make a circle with it. Then pill it tight between two fingers. The string length remains the same; that is the peripheral length. The areas are obviously different.

Answer 4

ofcourse not.
for example if you imagine a rectangle,
a 2m wide and 7m long rectangle, has the primeter of 2*(2+7)=18 and area of 2*7=14
while a 4m wide and 5m long rectangle has the same perimeter, but its area will be 4*5=20

ofcourse in some shapes, like a circle it is true.
means if the perimeter of two circles be equal, their area will be equal too.

Answer 5

No.
Consider a square / circle with the area.
Now you make a rectangle with nearly zero width having the same perimeter. It has nearly zero area.