Perimeter
Encyclopedia
A perimeter is a path that surrounds an area
. The word comes from the Greek peri (around) and meter (measure). The term may be used either for the path or its length - it can be thought of as the length of the outline of a shape. The perimeter of a circular area is called circumference
.
Calculating the perimeter has considerable practical applications. The perimeter can be used to calculate the length of fence required to surround a yard or garden. The perimeter of a wheel (its circumference) describes how far it will roll in one revolution. Similarly, the amount of string wound around a spool is related to the spool's perimeter.
Perimeter is about the distance around all of a shape. Perimeters for more general shapes can be calculated as any path with
where 
is the length of the path and 
is an infinitesimal line element. Both of these must be replaced with other algebraic forms in order to be solved: an advanced notion of perimeter, which includes hypersurface
s bounding volumes in
-dimensional euclidean space
s can be found in the theory of Caccioppoli set
s.
Area
Area is a quantity that expresses the extent of a two-dimensional surface or shape in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat...
. The word comes from the Greek peri (around) and meter (measure). The term may be used either for the path or its length - it can be thought of as the length of the outline of a shape. The perimeter of a circular area is called circumference
Circumference
The circumference is the distance around a closed curve. Circumference is a special perimeter.-Circumference of a circle:The circumference of a circle is the length around it....
.
Practical uses
Formulae
| shape | formula | variables |
|---|---|---|
| circle Circle A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius.... |
 |
where  is the radius. |
| triangle Triangle A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted .... |
 |
where  ,  and  are the lengths of the sides of the triangle. |
| square Square (geometry) In geometry, a square is a regular quadrilateral. This means that it has four equal sides and four equal angles... |
 |
where  is the side length |
| rectangle Rectangle In Euclidean plane geometry, a rectangle is any quadrilateral with four right angles. The term "oblong" is occasionally used to refer to a non-square rectangle... |
 |
where  is the length and  is the width |
| equilateral polygon |  |
where  is the number of sides and  is the length of one of the sides. |
| regular polygon Regular polygon A regular polygon is a polygon that is equiangular and equilateral . Regular polygons may be convex or star.-General properties:... |
 |
where  is the number of sides and  is the distance between center of the polygon and one of the verticesVertex (geometry) In geometry, a vertex is a special kind of point that describes the corners or intersections of geometric shapes.-Of an angle:... of the polygon. |
| general polygon Polygon In geometry a polygon is a flat shape consisting of straight lines that are joined to form a closed chain orcircuit.A polygon is traditionally a plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments... |
 |
where  is the length of the  -th (1st, 2nd, 3rd ... n-th) side of an n-sided polygon. |
Perimeter is about the distance around all of a shape. Perimeters for more general shapes can be calculated as any path with
where is the length of the path and is an infinitesimal line element. Both of these must be replaced with other algebraic forms in order to be solved: an advanced notion of perimeter, which includes hypersurfaceHypersurface
In geometry, a hypersurface is a generalization of the concept of hyperplane. Suppose an enveloping manifold M has n dimensions; then any submanifold of M of n − 1 dimensions is a hypersurface...
s bounding volumes in
-dimensional euclidean spaceEuclidean space
In mathematics, Euclidean space is the Euclidean plane and three-dimensional space of Euclidean geometry, as well as the generalizations of these notions to higher dimensions...
s can be found in the theory of Caccioppoli set
Caccioppoli set
In mathematics, a Caccioppoli set is a set whose boundary is measurable and has a finite measure. A synonym is set of finite perimeter...
s.
See also
- Isoperimetric inequality
- CircumferenceCircumferenceThe circumference is the distance around a closed curve. Circumference is a special perimeter.-Circumference of a circle:The circumference of a circle is the length around it....
- Caccioppoli setCaccioppoli setIn mathematics, a Caccioppoli set is a set whose boundary is measurable and has a finite measure. A synonym is set of finite perimeter...
- Pythagorean TheoremPythagorean theoremIn mathematics, the Pythagorean theorem or Pythagoras' theorem is a relation in Euclidean geometry among the three sides of a right triangle...
- Wetted perimeterWetted perimeterThe wetted perimeter is the perimeter of the cross sectional area that is "wet." The term wetted perimeter is common in Civil Engineering, Environmental Engineering and heat transfer applications; it is associated with the hydraulic diameter...
- AreaAreaArea is a quantity that expresses the extent of a two-dimensional surface or shape in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat...
- VolumeVolumeVolume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains....