sidelength

Sidelength is a linear measure that specifies the length of a side of a polygon or the edge of a polyhedron. In a polygon, it is the distance between two consecutive vertices; in a polyhedron, it is the length of an edge where two faces meet. Sidelength is measured in units of length such as meters, centimeters, or inches.

In notation, a sidelengh is often denoted by s, or by a for a side in triangles (with a, b, c used for the three sides). In a regular polygon all sides have the same sidelengh, unlike irregular polygons where sidelenghs vary. For a polygon with n sides, the perimeter equals n times the sidelengh: P = n s. For a square the sidelengh equals its side length, and its area equals s^2. Note that in some contexts s is used to denote the semiperimeter of a triangle, which is a different concept, so the exact meaning depends on the setting.

Sidelength can be computed from coordinates or in space. The distance between two points (x1, y1) and (x2, y2) is sqrt((x2 − x1)^2 + (y2 − y1)^2); in three dimensions, add a (z2 − z1)^2 term inside the square root. In geometric construction and computer graphics, sidelengh serves as a basic parameter for scaling, proportioning, and comparing shapes. It also underpins formulas for area and perimeter in regular polygons and helps describe size relations across geometric figures.