Perimeter

The perimeter is the distance around a given two-dimensional object. The word perimeter is a Greek root meaning measure around, or literally "around-measure".

Practical uses

Calculations of perimeter and area have considerable practical applications. Perimeter is used in calculating the border of an object such as a yard or flowerbed when a fence or other border is being installed around the edges. Area is used when all the area inside of a perimeter is being covered with something, such as a yard being covered with sod or fertilizer.

In military usage, the term perimeter defines a geographic area of importance, such as a physical installation or defensive work, but can also refer to a theoretical construct such as an all-round defense formed by a small group of soldiers, the purpose of which is mutual protection of each other rather than defence of actual territory.

Formulas

Polygons

As a general rule, the perimeter of a polygon can always be calculated by adding all the length of the sides together. So, the formula for triangles is $P=a+b+c$, where $a$, $b$ and $c$ stand for each side of it. For quadrilaterals the equation is $P=a+b+c+d$ or $P=a+b+a+b$. For equilateral polygons, $P=na$, where n is the number of sides and a is the measure of the side.

Circles

For circles the equation is

$$

 P = 2 pi r

or

$$

 P = pi d

where $P$ is the perimeter, $r$ is the circle's radius, $pi$ is the mathematical constant pi, and $d$ is the circle's diameter.

In general

If r is considered to be the distance from the center of a regular polygon to one of its vertices (or in the case of a circle, the radius), the following holds true:

$P\; =\; frac\{dA\}\{dr\}$

• $P$ stands for the perimeter,
• $d$ stands for the differential operator
• $r$ stands for the radius
• $A$ stands for the area

See also

• Isoperimetric inequality
• Circumference
• Pythagorean Theorem
• Wetted perimeter

External links