geometry, the semiperimeter of a polygon is half its perimeter. Although it has such a simple derivation from the perimeter, the semiperimeter appears frequently...
6 KB (890 words) - 18:19, 18 April 2024
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)...
19 KB (3,519 words) - 17:47, 13 August 2024
− 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}}...
7 KB (1,331 words) - 09:15, 15 March 2024
Right triangle (section Sides and semiperimeter)
{\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...
18 KB (2,951 words) - 15:04, 12 August 2024
= 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...
35 KB (5,710 words) - 01:35, 12 September 2024
perimeter into two equal lengths, this common length being called the semiperimeter of the triangle. The three splitters of a triangle all intersect each...
11 KB (1,302 words) - 19:39, 25 September 2024
( 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...
25 KB (3,092 words) - 09:41, 8 September 2024
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...
31 KB (4,082 words) - 00:12, 11 July 2024
(orig. 1960). Gutierrez, Antonio, "Hexagon, Inscribed Circle, Tangent, Semiperimeter", [1] Archived 2012-05-11 at the Wayback Machine, Accessed 2012-04-17...
30 KB (2,669 words) - 03:46, 28 September 2024
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):...
16 KB (1,719 words) - 20:12, 15 September 2024
= 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)}}...
54 KB (6,396 words) - 02:22, 10 October 2024
The parameters in a triangle inequality can be the side lengths, the semiperimeter, the angle measures, the values of trigonometric functions of those...
44 KB (9,295 words) - 08:24, 20 September 2024
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...
48 KB (6,876 words) - 11:23, 23 September 2024
, 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...
18 KB (2,326 words) - 22:08, 4 September 2024
tangential quadrilateral add up to the same total length, which equals the semiperimeter s of the quadrilateral: a + c = b + d = a + b + c + d 2 = s . {\displaystyle...
34 KB (4,964 words) - 22:53, 13 February 2023
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...
13 KB (2,153 words) - 09:46, 10 September 2024
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...
20 KB (3,530 words) - 09:55, 20 September 2024
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...
34 KB (5,176 words) - 13:40, 1 July 2024
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,...
81 KB (11,397 words) - 20:39, 1 September 2024
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...
147 KB (17,481 words) - 05:04, 23 September 2024
Nagel point intersection of lines from each vertex to the corresponding semiperimeter point X(9) Mittenpunkt symmedian point of the triangle formed by the...
6 KB (346 words) - 05:00, 11 August 2024
coordinate system Pole Real axis Secant line Circular sector or "sector" Semiperimeter Symmetry Shape Pattern Crystal system Frieze group Isometry Lattice...
13 KB (910 words) - 13:17, 13 September 2024
{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...
77 KB (10,607 words) - 05:07, 2 October 2024
\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...
87 KB (9,766 words) - 15:22, 8 October 2024
)]}}.} Here, a, b, c, d are the sides of the quadrilateral, s is the semiperimeter, and α and γ are any two opposite angles, since cos ( α + γ ) = cos...
6 KB (1,240 words) - 17:07, 14 August 2024
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...
11 KB (1,414 words) - 11:53, 11 September 2024
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...
15 KB (2,225 words) - 04:09, 17 September 2024
+ 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...
6 KB (927 words) - 15:12, 7 April 2023
lengths of opposite sides are the same. Both sums of lengths equal the semiperimeter of the quadrilateral. The converse implication is also true: whenever...
3 KB (361 words) - 01:34, 8 October 2024
side lengths of a triangle are a , b , c {\displaystyle a,b,c} , the semiperimeter s = ( a + b + c ) / 2 , {\displaystyle s=(a+b+c)/2,} and A is the angle...
20 KB (3,087 words) - 15:16, 19 February 2024