Difference between revisions of "Semiperimeter"
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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]]. | ||
Revision as of 23:28, 30 December 2020
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 
.
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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.
