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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.
where K is the area of the quadrilateral and s is its semiperimeter. For a tangential quadrilateral with given sides, the inradius is maximum when the quadrilateral is also cyclic (and hence a bicentric quadrilateral). In terms of the tangent lengths, the incircle has radius [8]: Lemma2 [14]
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 ...
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
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 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 ...
A triangle with sides <, semiperimeter = (+ +), area, altitude opposite the longest side, circumradius, inradius, exradii,, tangent to ,, respectively, and medians,, is a right triangle if and only if any one of the statements in the following six categories is true. Each of them is thus also a property of any right triangle.