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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.
In this case, the semiperimeter will equal the longest side, causing Heron's formula to equal zero. If one of three given lengths is greater than the sum of the other two, then they violate the triangle inequality and do not describe the sides of a Euclidean triangle. In this case, Heron's formula gives an imaginary result.
According to T. A. Ivanova (in 1976), the semiperimeter s of a tangential quadrilateral satisfies where r is the inradius. There is equality if and only if the quadrilateral is a square. [13] This means that for the area K = rs, there is the inequality
Add a calculator widget to the page. Like a spreadsheet you can refer to other widgets in the same page. Template parameters [Edit template data] Parameter Description Type Status id id The id for this input. This is used to reference it in formula of other calculator templates String required type type What type of input box Suggested values plain number text radio checkbox passthru hidden ...
where r is the inradius, and s is the semiperimeter (in fact, this formula holds for all tangential polygons), and [15]: Lemma 2 = = = where ,, are the radii of the excircles tangent to sides a, b, c respectively. We also have
where s, the semiperimeter, is defined to be = + + +. This formula generalizes Heron's formula for the area of a triangle. A triangle may be regarded as a ...
No description. Template parameters [Edit template data] Parameter Description Type Status float float Float on the left or right of the page Suggested values left right none Default left Example right String optional caption caption Caption for calculator widget Content optional The above documentation is transcluded from Template:Calculator layout/doc. (edit | history) Editors can experiment ...
The parameters most commonly appearing in triangle inequalities are: the side lengths a, b, and c;; the semiperimeter s = (a + b + c) / 2 (half the perimeter p);; the angle measures A, B, and C of the angles of the vertices opposite the respective sides a, b, and c (with the vertices denoted with the same symbols as their angle measures);