Perimeter of the polygon

A perimeter is a path that surrounds a two-dimensional shape. 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 circle or ellipse is called its circumference.

Calculating the perimeter has several practical applications. A calculated perimeter is 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.

The perimeter is the distance around a shape. Perimeters for more general shapes can be calculated, as any path, with ${\displaystyle \int _{0}^{L}\mathrm {d} s}$, where ${\displaystyle L}$ is the length of the path and ${\displaystyle ds}$ is an infinitesimal line element. Both of these must be replaced with by algebraic forms in order to be practically calculated. If the perimeter is given as a closed piecewise smooth plane curve ${\displaystyle \gamma :[a,b]\rightarrow \mathbb {R} ^{2}}$ with

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