geometry, the semiperimeter of a polygon is half its perimeter. Although it has such a simple derivation from the perimeter, the semiperimeter appears frequently...

⁠ ⁠ c . {\displaystyle c.} ⁠ Letting ⁠ s {\displaystyle s} ⁠ be the semiperimeter of the triangle, s = 1 2 ( a + b + c ) , {\displaystyle s={\tfrac {1}{2}}(a+b+c)...

{\displaystyle \triangle ABC} with sides a ≤ b < c {\displaystyle a\leq b<c} , semiperimeter s = 1 2 ( a + b + c ) {\textstyle s={\tfrac {1}{2}}(a+b+c)} , area T...

− d ) {\displaystyle K={\sqrt {(s-a)(s-b)(s-c)(s-d)}}} where s, the semiperimeter, is defined to be s = a + b + c + d 2 . {\displaystyle s={\frac {a+b+c+d}{2}}...

= 1 2 ( a + b + c ) {\displaystyle s={\tfrac {1}{2}}(a+b+c)} is the semiperimeter. The tangency points of the incircle divide the sides into segments...

perimeter into two equal lengths, this common length being called the semiperimeter of the triangle. The three splitters of a triangle all intersect each...

( a + b + c + d ) {\displaystyle s={\tfrac {1}{2}}(a+b+c+d)} is the semiperimeter of the trapezoid. (This formula is similar to Brahmagupta's formula...

The parameters in a triangle inequality can be the side lengths, the semiperimeter, the angle measures, the values of trigonometric functions of those...

(orig. 1960). Gutierrez, Antonio, "Hexagon, Inscribed Circle, Tangent, Semiperimeter", [1] Archived 2012-05-11 at the Wayback Machine, Accessed 2012-04-17...

d ) {\displaystyle K={\sqrt {(s-a)(s-b)(s-c)(s-d)}}\,} where s, the semiperimeter, is s = ⁠1/2⁠(a + b + c + d). This is a corollary of Bretschneider's...

inequality holding for an obtuse triangle. For an acute triangle with semiperimeter s,: p.115, #2874  s − r > 2 R , {\displaystyle s-r>2R,} and the reverse...

q: K = p ⋅ q 2 , {\displaystyle K={\frac {p\cdot q}{2}},} or as the semiperimeter times the radius of the circle inscribed in the rhombus (inradius):...

vertex at the right angle. For any triangle with sides a, b, c and semiperimeter s = 1 2 ( a + b + c ) , {\displaystyle s={\tfrac {1}{2}}(a+b+c),} the...

where the sides in sequence are a, b, c, d, where s is the semiperimeter, and A and C are two (in fact, any two) opposite angles. This reduces...

coordinate system Pole Real axis Secant line Circular sector or "sector" Semiperimeter Symmetry Shape Pattern Crystal system Frieze group Isometry Lattice...

+ c ) {\textstyle 2{\sqrt {bcs(s-a)}}{\big /}(b+c)} where s is the semiperimeter (and likewise for the other angles' bisectors). Any altitude dropped...

b,c)<a+b+c} and thus that the longest side length is less than the semiperimeter. A mathematically equivalent formulation is that the area of a triangle...

, R ( z ) {\displaystyle R(z),R(z)} and l 1 {\displaystyle l_{1}} (semiperimeter R ( z ) + l 1 ( z ) / 2 {\displaystyle R(z)+l_{1}(z)/2} ) plus n {\displaystyle...

s = 1 2 ( a + b + c ) {\textstyle s={\tfrac {1}{2}}(a+b+c)} is the semiperimeter, or half of the triangle's perimeter. Three other equivalent ways of...

radius of the outer Soddy circle of any right triangle is equal to its semiperimeter. The outer Soddy center is located at D, where ACBD is a rectangle,...

line segment from the orthocenter to the circumcenter as e, and the semiperimeter as s, the following inequalities hold: d s < d u < d v < 1 3 ; {\displaystyle...

In the earliest usages, the Greek letter π was used to denote the semiperimeter (semiperipheria in Latin) of a circle and was combined in ratios with...

Nagel point intersection of lines from each vertex to the corresponding semiperimeter point X(9) Mittenpunkt symmedian point of the triangle formed by the...

+ c {\displaystyle d={\frac {2{\sqrt {bcs(s-a)}}}{b+c}}} where the semiperimeter s = a + b + c 2 . {\displaystyle s={\tfrac {a+b+c}{2}}.} The side of...

{A-B}{2}}}{\tan {\frac {A+B}{2}}}}={\frac {a-b}{a+b}}} . If s is the triangle's semiperimeter, (a + b + c)/2, and r is the radius of the triangle's incircle, then...

= 1 2 ( a + b + c ) {\displaystyle s={\tfrac {1}{2}}(a+b+c)} be the semiperimeter, T = s ( s − a ) ( s − b ) ( s − c ) . {\displaystyle T={\sqrt {s(s-a)(s-b)(s-c)}}...

supplementary. A cyclic quadrilateral with successive sides a, b, c, d and semiperimeter s = (a + b + c + d) / 2 has its circumradius given by R = 1 4 ( a b...

the given triangle. The perimeter of the medial triangle equals the semiperimeter (half the perimeter) of the original triangle, and its area is one quarter...

\textstyle k={\sqrt {s(s-a)(s-b)(s-c)}}} , where s {\displaystyle s} is the semiperimeter – was known to Archimedes several centuries before Heron lived. Arabic...

with very sharp angles, because of the near-cancellation between the semiperimeter and side length in those triangles. If the apex angle ( θ ) {\displaystyle...