# Geometry: Measurements

### Perimeter

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:

Figure %: Various 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.

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