The perimeter of any region in a plane
is the length of the curve or curves that bound the
region. For regions that aren't bound by line
segments, the perimeter often requires
calculus to calculate. For polygons, the name
regions that are bound by line segments, perimeter is easy to calculate. The
perimeter of a polygon is simply the sum of the lengths of all the line segments
that bound the polygon. Here are some polygons and their perimeters:

For certain polygons whose sides, by definition,
have special relationships with one another, perimeter can be calculated without
knowing the length of every single side.

The perimeter of an n-sided regular polygon is
equal to n times the length of any one side. This is true, of course, because
all of the sides of a regular polygon are
congruent.

The perimeter of a square or a
rhombus is four times the length of any one side.

The perimeter of a parallelogram or a
rectangle is two times the sum of the lengths of
any two adjacent sides. This holds true because
opposite sides of these figures are congruent.

Perimeter, of course, does not depend on whether a polygon is
convex or concave; it
only depends on the lengths of the sides of a polygon. For polygons that don't
fit into any of the categories above, it is necessary to know the lengths of all
of the sides in order to calculate perimeter.