Equilateral Triangle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

equilateral triangle 1

  • A two-dimensional figure that has three sides that are the same length and all sides and angles are congruent.
  • A equilateral triangle is a polygon.
  • Angle bisector of a equilateral triangle is a line that splits an angle into two equal angles.
  • Height of a equilateral triangle is the length of the two sides and the perpendicular height of the 90 degree angle.
  • Median of a equilateral triangle is a line segment from a vertex (coiner point) to the midpoint of the opposite side.
  • Radius of a circumcircle (outer) of a equilateral triangle if given legs and hypotrnuse ( R ).
  • Radius of a inscribed circle (inner) of a equilateral triangle if given legs and hypotrnuse ( r ).
  • Semiperimeter of a equilateral triangle is one half of the perimeter.
  • \(x\;+\;y\;+\;z\;=\;180°\).
  • 3 edges
  • 3 vertexs
  • Sidess:  \(a\),  \(b\),  \(c\)
  • Angles:  \(A\),  \(B\),  \(C\)
  • Area:  \(K\)
  • Perimeter:  \(P\)
  • Height:  \(h_a\),  \(h_b\),  \(h_c\)
  • Median:  \(m_a\),  \(m_b\),  \(m_c\)  -  A line segment from a vertex (corner point) to the midpoint of the opposite side
  • Angle bisectors:  \(t_a\),  \(t_b\),  \(t_c\)  -  A line that splits an angle into two equal angles
  • Semi-perimeter:  \(s\)  -  One half of the perimeter
  • Inradius of triangle:  \(r\)
  • Outradius (circumcircle) of triangle:  \(R\)

equilateral triangle 4Angle bisector of an Equilateral Triangle formula

\(\large{ t_a, t_b, t_c = a \; \sqrt {  \frac { 3 }{ 2 }   } }\)

Where:

\(\large{ t_a, t_b, t_c }\) = angle bisector

\(\large{ a }\) = side

 

 

equilateral triangle 1Area of an Equilateral Triangle formula

\(\large{ K =\frac { \sqrt {3} } {4}\; a^2 }\)

Where:

\(\large{ K }\) = area

\(\large{ a }\) = side

 

 

equilateral triangle 3Circumcircle of an Equilateral Triangle formula

\(\large{ R =  \frac  { a } { \sqrt {3 } }  }\)

\(\large{ R =  \frac  { 2\;h } { 3 }   }\)

Where:

\(\large{ R }\) = outcircle

\(\large{ a }\) = side

\(\large{ h }\) = height

equilateral triangle 4Height of an Equilateral Triangle formula

\(\large{ h_a, h_b, h_c = a  \sqrt {  \frac { 3 }{ 2 }   } }\)

Where:

\(\large{ h_a, h_b, h_c }\) = height

\(\large{ a }\) = side

 

 

equilateral triangle 3Inscribed Circle of an Equilateral Triangle formula

\(\large{ r =   \frac  { a  }  {  2\;  \sqrt { 3 }  }  }\)

Where:

\(\large{ r }\) = incircle

\(\large{ a }\) = side

 

 

equilateral triangle 4Median of an Equilateral Triangle formula

\(\large{ m_a, m_b, m_c = a \; \sqrt {  \frac { 3 }{ 2 }   } }\)

Where:

\(\large{ m_a, m_b, m_c }\) = median

\(\large{ a }\) = side

 

 

equilateral triangle 1Perimeter of an Equilateral Triangle formula

\(\large{ P = 3\;a }\)

Where:

\(\large{ P }\) = perimeter

\(\large{ a }\) = side

 

 

equilateral triangle 1Semiperimeter of an Equilateral Triangle formula

\(\large{ s =   \frac  { a + b + c }  { 2  }   }\)

Where:

\(\large{ s }\) = semiperimeter

\(\large{ a, b, c }\) = side

 

 

equilateral triangle 1Side of an Equilateral Triangle formula

\(\large{ a = \frac {P}{3} }\)

\(\large{ a = \frac {2}{3}\; 3^{3/4} \sqrt K }\)

Where:

\(\large{ a }\) = side

\(\large{ P }\) = perimeter

\(\large{ K }\) = area

 

Tags: Equations for Triangle