Polygon

Written by Jerry Ratzlaff on . Posted in Plane Geometry

A regular polygon has equal side lengths and angle degrees.polygon

Central Angle formula

\(\phi =\frac {2 \pi}{ n} \)

Where:

\(\phi\) = central angle in radians

\(\pi\) = Pi

\(n\) = equal sides (number of)

Vertex Angle formula

\(\theta =\frac { \pi \left (n-2 \right) } {n} = \pi - \phi \)

Where:

\(\theta\) = vertex angle

\(\pi\) = Pi

\(n\) = equal sides (number of)

\(\phi\) = central angle in radians

Side Length formula

\(s= 2r \left( tan \left( \frac{\theta}{2} \right) \right)\)

Where:

\(s\) = side length

\(tan\) = tangent

\(r\) = radius

\(\theta\) = vertex angle

Perimeter formula

\(p=ns \)

Where:

\(p\) = perimeter

\(n\) = equal sides (number of)

\(s\) = side length

Area formula

\(A=\frac{1}{2} nsr \)

Where:

\(n\) = equal sides (number of)

\(s\) = side length

\(r\) = radius

Types of Regular Polygon

  • Triangle - 3 sides - 60° interior angle
  • Quadrilateral - 4 sides - 90° interior angle
  • Pentagon - 5 sides - 108° interior angle
  • Hexagon - 6 sides - 120° interior angle
  • Heptagon - 7 sides - 128.571° interior angle
  • Octagon - 8 sides - 135° interior angle
  • Nonagon - 9 sides - 140° interior angle
  • Decagon - 10 sides - 144° interior angle
  • Hendecagon - 11 sides - 147.273° interior angle
  • Dodecagon - 12 sides - 150° interior angle
  • Triskaidecagon - 13 sides - 152.308° interior angle
  • Tetrakaidecagon - 14 sides - 154.286° interior angle
  • Pentadecagon - 15 sides - 156° interior angle
  • Hexakaidecagon - 16 sides - 157.5° interior angle
  • Heptadecagon - 17 sides - 158.824° interior angle
  • Octakaidecagon - 18 sides - 160° interior angle
  • Enneadecagon - 19 sides - 161.053° interior angle
  • Cosagon - 20 sides - 162° interior angle