Polygons
Polygons are fundamental to determine perimeters, not only because they are the simplest shapes but also because the perimeters of many shapes are calculated approximating them by sequences of polygons tending to these shapes. The first mathematician known to having used this kind of reasoning is Archimedes, who approximated the perimeter of a circle surrounding it by regular polygons.
The perimeter of a polygon equals the sum of the lengths of its edges. In particular, the perimeter of a rectangle which width is and length is equal to .
An equilateral polygon is a polygon which has all sides of the same length (for example, a rhombus is a 4-sided equilateral polygon). To calculate the perimeter of an equilateral polygon, one must multiply the length of the sides by their number.
A regular polygon may be defined by the number of its sides and by its radius, that is to say, the constant distance between its centre and each of its vertices. One can calculate the length of its sides using trigonometry. If R is a regular polygon's radius et n the number of its sides, then its perimeter is
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