# Equilateral Triangle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

• 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:  $$R$$

### Angle 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

### Area of an Equilateral Triangle formula

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

Where:

$$\large{ K }$$ = area

$$\large{ a }$$ = side

### Circumcircle 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

### Height 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

### Inscribed Circle of an Equilateral Triangle formula

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

Where:

$$\large{ r }$$ = incircle

$$\large{ a }$$ = side

### Median 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

### Perimeter of an Equilateral Triangle formula

$$\large{ P = 3\;a }$$

Where:

$$\large{ P }$$ = perimeter

$$\large{ a }$$ = side

### Semiperimeter of an Equilateral Triangle formula

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

Where:

$$\large{ s }$$ = semiperimeter

$$\large{ a, b, c }$$ = side

### Side 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