Perimeter
Encyclopedia
A perimeter is a path that surrounds an area
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

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.

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 vertices
Vertex (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 hypersurface
Hypersurface
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 space
Euclidean 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
  • 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....

  • 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...

  • Pythagorean Theorem
    Pythagorean theorem
    In mathematics, the Pythagorean theorem or Pythagoras' theorem is a relation in Euclidean geometry among the three sides of a right triangle...

  • Wetted perimeter
    Wetted perimeter
    The 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...

  • Area
    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...

  • Volume
    Volume
    Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains....

The source of this article is wikipedia, the free encyclopedia.  The text of this article is licensed under the GFDL.
 
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