Editing Semiperimeter (section)

=== For triangles ===
The area {{mvar|A}} of any triangle is the product of its [[inradius]] (the radius of its inscribed circle) and its semiperimeter:

:<math> A = rs.</math>

The area of a triangle can also be calculated from its semiperimeter and side lengths {{mvar|a, b, c}} using [[Heron's formula]]:

:<math>A = \sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}.</math>

The [[circumradius]] {{mvar|R}} of a triangle can also be calculated from the semiperimeter and side lengths:
:<math>R = \frac{abc} {4\sqrt{s(s-a)(s-b)(s-c)}}.</math>
This formula can be derived from the [[law of sines]].

The inradius is

: <math>r = \sqrt{\frac{(s-a)(s-b)(s-c)}{s}}. </math>

The [[law of cotangents]] gives the [[cotangent]]s of the half-angles at the vertices of a triangle in terms of the semiperimeter, the sides, and the inradius.

The length of the [[Bisection#Angle bisector|internal bisector of the angle]] opposite the side of length {{mvar|a}} is<ref name=Johnson>{{cite book|last=Johnson|first=Roger A.|title=Advanced Euclidean Geometry|year=2007|publisher=Dover|location=Mineola, New York|isbn=9780486462370|page=70}}</ref>

:<math>t_a= \frac{2 \sqrt{bcs(s-a)}}{b+c}.</math>

In a [[right triangle]], the radius of the [[excircle]] on the [[hypotenuse]] equals the semiperimeter. The semiperimeter is the sum of the inradius and twice the circumradius. The area of the right triangle is <math>(s-a)(s-b)</math> where {{mvar|a, b}} are the legs.