Difference between revisions of "Semiperimeter"

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The '''semiperimeter''' of a figure is one half of the [[perimeter]], or
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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>.
<math>\frac{P}{2}</math>, where <math>P</math> is the total perimeter of a figure.
 
  
  
 
==Applications==
 
==Applications==
The semiperimeter has many uses in geometeric formulas. Two well known examples are [[Heron's formula]] and [[Brahmagupta's formula]]. It frequently shows up in triangle problems.
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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). 
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Two other well-known examples of formulas involving the semiperimeter are [[Heron's formula]] and [[Brahmagupta's formula]].

Revision as of 12:55, 6 July 2006

The semiperimeter of a geometric figure is one half of the perimeter, or $\frac{P}{2}$, where $P$ is the total perimeter of a figure. It is typically denoted $s$.


Applications

The semiperimeter has many uses in geometric formulas. Perhaps the simplest is $A=rs$, where $A$ is the area of a triangle and $r$ 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.