Regular Heptagon

Written by Jerry Ratzlaff on . Posted in Plane Geometry

  • regular heptagon 2Regular heptagon (a two-dimensional figure) is a polygon with seven 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 51.429°
  • Interior angles are 128.571°
  • 14 diagonals
  • 7 edges
  • 7 vertexs

Area of a Regular Heptagon formula

\(\large{ A_{area} = \frac {7} {4} \;a^2 \; \cot \;\left( \frac {180°} {7} \right)   }\)

Where:

\(\large{ A_{area} }\) = area

\(\large{ a }\) = edge

\(\large{ \cot }\) = cotangent

Edge of a Regular Heptagon formula

\(\large{ a = \frac {p}{7}   }\)

Where:

\(\large{ a }\) = edge

\(\large{ p }\) = perimeter

Perimeter of a Regular Heptagon formula

\(\large{ p= 7 \;a }\)

Where:

\(\large{ p }\) = perimeter

\(\large{ a }\) = edge