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For a triangle with side lengths $a,b,c$ and semiperimeter $s=(a+b+c)/2$, its area is $A=\sqrt{s(s-a)(s-b)(s-c)}$. This expresses the area using only the three side lengths.

The inradius is the radius of an incircle. For a triangle of area $A$ and semiperimeter $s$, it is $r=A/s$: joining the incenter to the three vertices partitions the triangle into three triangles with common altitude $r$.