Difference between revisions of "Semiperimeter"
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| − | The '''semiperimeter''' of a geometric figure is one half of the [[perimeter]], or <math>\frac{P}{2}</math>, where <math>P</math> is the total perimeter of a figure. It is typically denoted <math>s</math>. | + | The '''semiperimeter''' of a geometric figure is one half of the [[perimeter]], or <math>\frac{P}{2}</math>, where <math>P</math> is the total perimeter of a figure. It is typically denoted <math>s</math>. In a triangle, it has uses in formulas for the lengths relating the [[excenter]] and [[incenter]]. |
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==Applications== | ==Applications== | ||
The semiperimeter has many uses in geometric formulas. Perhaps the simplest is <math>A=rs</math>, where <math>A</math> is the [[area]] of a [[triangle]] and <math>r</math> is the triangle's [[inradius]] (that is, the [[radius]] of the [[circle]] [[inscribed]] in the triangle). | The semiperimeter has many uses in geometric formulas. Perhaps the simplest is <math>A=rs</math>, where <math>A</math> is the [[area]] of a [[triangle]] and <math>r</math> is the triangle's [[inradius]] (that is, the [[radius]] of the [[circle]] [[inscribed]] in the triangle). | ||
Two other well-known examples of formulas involving the semiperimeter are [[Heron's formula]] and [[Brahmagupta's formula]]. | Two other well-known examples of formulas involving the semiperimeter are [[Heron's formula]] and [[Brahmagupta's formula]]. | ||
Latest revision as of 15:19, 11 July 2024
The semiperimeter of a geometric figure is one half of the perimeter, or 
, where 
is the total perimeter of a figure. It is typically denoted 
. In a triangle, it has uses in formulas for the lengths relating the excenter and incenter.
This article is a stub. Help us out by expanding it.
Applications
The semiperimeter has many uses in geometric formulas. Perhaps the simplest is 
, where 
is the area of a triangle and 
is the triangle's inradius (that is, the radius of the circle inscribed in the triangle).
Two other well-known examples of formulas involving the semiperimeter are Heron's formula and Brahmagupta's formula.
