In general the larger the perimeter (of a flat shape) the greater the area. Given two congruent shapes the one with the larger perimeter has a greater area.
But two shapes that are not congruent (or almost so) do not follow this rule: for example a rectangle fifteen units long and one unit wide has an area of 15 square units and a perimeter of 32 units. While a square with edges four units has an area of sixteen square units (one more than the other rectangle) but a perimeter of only sixteen units (half that of the long thin rectangle).
So too with surface area and volume. Of two congruent 3 dimensional shapes, the one with the larger volume will also have a larger surface area.
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They are characteristics of geometric shapes. However, there is no simple relationship. A rectangle with a given perimeter can have a whole range of areas.
Area is a 2-dimensional measure. Perimeter is 1-dimensional and volume is 3-dimensional.
Neither. -- Perimeter = the distance all the way around it. -- Area = how much of the floor it covers. -- Volume = how much water it can hold.
Volume is the amount of liquid a container can hold. Perimeter is the length of the borders outside a 2D figure. Area is the total space in a 2D shape.
Perimeter is a length, not an area or volume...