What is Semi-Perimeter?

In geometry, the semiperimeter of a polygon is half its perimeter. Although it has such a simple derivation from the perimeter, the semiperimeter appears frequently enough in formulas for triangles and other figures that it is given a separate name. When the semiperimeter occurs as part of a formula, it is typically denoted by the letter s.

Triangles

In any triangle, the distance around the triangle from a vertex to the point on the opposite edge touched by an excircle equals the semiperimeter.

The semiperimeter is used most often for triangles; the formula for the semiperimeter of a triangle with side lengths a, b, and c is