Equilateral Triangle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

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  • An equilateral triangle is when all three angles are equal.
  • A equilateral triangle is a polygon.
  • The total of angles equal
  • \(x\;+\;y\;+\;z\;=\;180°\).
  • 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 (coiner 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:  \(R\)

Angle bisector of an Equilateral Triangle

An angle bisector is a line that splits an angle into two equal angles.

Angle bisector of an Equilateral Triangle formula

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

Where:

\(t_a, t_b, t_c\) = angle bisector

\(a\) = side

Area of an Equilateral Triangle

Area of an Equilateral Triangle formula

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

Where:

\(K\) = area

\(a\) = side

Circumcircle of an Equilateral Triangle

The radius of a circumcircle (outer) of a an equilateral triangle if given side and height \(( R )\).

Circumcircle of an Equilateral Triangle formula

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

\(R =  \frac  { 2h } { 3 }   \)

Where:

\(R\) = outcircle

\(a\) = side

\(h\) = height

Height of an Equilateral Triangle

Height is the length of the two sides and the perpendicular height of the 90 degree angle.

Height of an Equilateral Triangle formula

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

Where:

\(h_a, h_b, h_c\) = height

\(a\) = side

Inscribed Circle of an Equilateral Triangle

The radius of a inscribed circle (inner) of an equilateral triangle if given side \(( r )\).

Inscribed Circle of an Equilateral Triangle formula

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

Where:

\(r\) = incircle

\(a\) = side

Median of an Equilateral Triangle

Median is a line segment from a vertex (coiner point) to the midpoint of the opposite side.

Median of an Equilateral Triangle formula

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

Where:

\(m_a, m_b, m_c\) = median

\(a\) = side

Perimeter of an Equilateral Triangle

Perimeter of an Equilateral Triangle formula

\(P = 3a \)

Where:

\(P\) = perimeter

\(a\) = side

Semiperimeter of an Equilateral Triangle

One half of the perimeter.

Semiperimeter of an Equilateral Triangle formula

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

Where:

\(s\) = semiperimeter

\(a, b, c\) = side

Side of an Equilateral Triangle

Side of an Equilateral Triangle formula

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

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

Where:

\(a\) = side

\(P\) = perimeter

\(K\) = area

 

Tags: Equations for Triangle