Apothem

on . Posted in Geometry

  • apothemApothem is the length of a line perpendicular from the center to the midpoint of the side of a regular polygon.
  • A irregular polygon has no center so there can be no apothem.

 

Apothem Edge formula

\(\large{A=\frac {s} {2 \;tan\; \left( \frac{180}{n} \right) } }\)
Symbol English Metric
\(\large{A}\) = apothem \(\large{in}\) \(\large{mm}\)
\(\large{s}\) = edge (side length) \(\large{in}\) \(\large{mm}\)
\(\large{n}\) = number of sides \(\large{dimensionless}\)
\(\large{tan}\) = tangent \(\large{deg}\) \(\large{rad}\)

 

Apothem Radius formula

\(\large{A= r \;cos\; {\left( \frac{180}{n} \right) } }\)
Symbol English Metric
\(\large{A}\) = apothem \(\large{in}\) \(\large{mm}\)
\(\large{cos}\) = cosine \(\large{deg}\) \(\large{rad}\)
\(\large{n}\) = number of sides \(\large{dimensionless}\)
\(\large{r}\) = radius \(\large{in}\) \(\large{mm}\)

 

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