Regular Pentagon

Written by Jerry Ratzlaff on . Posted in Plane Geometry

  • regular pentagon 1Regular pentagon (a two-dimensional figure) is a polygon with five congruent sides.
  • Circumcircle is a circle that passes through all the vertices of a two-dimensional figure.
  • Congruent is all sides having the same lengths and angles measure the same.
  • Diagonal is a line from one vertices to another that is non adjacent.
  • Inscribed circle is the largest circle possible that can fit on the inside of a two-dimensional figure.
  • Polygon (a two-dimensional figure) is a closed plane figure for which all edges are line segments and not necessarly congruent.
  • Exterior angles are 72°.
  • Interior angles are 108°.
  • 3 triangles created from any one vertex.
  • Diagonals do not cross the center point of the pentagon.
  • 5 diagonals
  • 5 edges
  • 5 vertexs

Area of a Regular Pentagon formula

\(\large{ A_{area} = \frac {a\;r}{2} }\)

Where:

\(\large{ A_{area} }\) = area

\(\large{ a }\) = edge

\(\large{ r }\) = inside radius

Circumcircle Radius of a Regular Pentagon formula

\(\large{ R =  \frac{a}{2} \; csc \; \frac{180°}{n}   }\)

Where:

\(\large{ R }\) = outside radius

\(\large{ a }\) = edge

\(\large{ n }\) = number of edges

Diagonal of a Regular Pentagon formula

\(\large{ D' = \frac{ 1 \;+\; \sqrt { 5} }{2} \; a   }\)

Where:

\(\large{ D' }\) = diagonal

\(\large{ a}\) = edge

Edge of a Regular Pentagon formula

\(\large{ a = 25^{3/4}\; \frac { \sqrt{A_{area}} }   { 5\; \left( \sqrt {20} \;+\; 5 \right) ^{1/4 } }   }\)

\(\large{ a = D' \;\frac { -1 \;+\; \sqrt { 5} }   {2}   }\)

Where:

\(\large{ a }\) = edge

\(\large{ A_{area} }\) = area

\(\large{ D' }\) = diagonal

Inscribed Circle Radius of a Regular Pentagon formula

\(\large{ r =  \frac{a}{2} \; cot \; \frac{180°}{n}   }\)

Where:

\(\large{ R }\) = outside radius

\(\large{ a }\) = edge

\(\large{ n }\) = number of edges

Perimeter of a Regular Pentagon formula

\(\large{ p= 5 \;a }\)

Where:

\(\large{ p }\) = perimeter

\(\large{ a }\) = edge