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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.

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

The area of any triangle is the product of its inradius and its semiperimeter; the same area formula also applies to tangential quadrilaterals, in which pairs of opposite sides have lengths adding to the semiperimeter. The area of a triangle can also be calculated from its semiperimeter and side lengths using Heron's formula:

The simplest form of Brahmagupta's formula, for the area of a cyclic quadrilateral, has a similar form:

The circumradius R of a triangle can also be calculated from the semiperimeter and side lengths:

This formula can be derived from the law of sines.