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Semiperimeter

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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.

Looking for a challenging algebra text? Preparing for MATHCOUNTS or the AMC exams?
Check out Art of Problem Solving's Introduction to Algebra by Richard Rusczyk.
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