Equilateral Triangle
- Equilateral triangle (a two-dimensional figure) 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.
- Circumcircle is a circle that passes through all the vertices of a two-dimensional figure.
- Height of a equilateral triangle is the length of the two sides and the perpendicular height of the 90 degree angle.
- Inscribed circle is the largest circle possible that can fit on the inside of a two-dimensional figure.
- Median of a equilateral triangle is a line segment from a vertex (coiner point) to the midpoint of the opposite side.
- Semiperimeter is one half of the perimeter.
- x + y + z = 180°
- 3 edges
- 3 vertexs
- Sides: a, b, c
- Angles: ∠A, ∠B, ∠C
- 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
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
\(\large{ a,\; b, \;c }\) = edge
area of an Equilateral triangle formula
\(\large{ A_{area} = \frac{ \sqrt{3} }{4}\; a^2 }\) |
Where:
\(\large{ A_{area} }\) = area
\(\large{ a, \;b, \;c }\) = edge
circumcircle of an Equilateral triangle formulas
\(\large{ R = \frac{ a }{ \sqrt {3 } } }\) | |
\(\large{ R = \frac{ 2\;h }{ 3 } }\) |
Where:
\(\large{ R }\) = outcircle
\(\large{ a, \;b, \;c }\) = edge
\(\large{ h }\) = 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
\(\large{ a, \;b, \;c }\) = edge
inscribed circle of an Equilateral triangle formula
\(\large{ r = \frac{ a }{ 2\; \sqrt{ 3 } } }\) |
Where:
\(\large{ r }\) = incircle
\(\large{ a, \;b,\; c }\) = edge
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
\(\large{ a,\; b,\; c }\) = edge
perimeter of an Equilateral triangle formula
\(\large{ P = 3\;a }\) |
Where:
\(\large{ P }\) = perimeter
\(\large{ a,\; b, \;c }\) = edge
semiperimeter of an Equilateral triangle formula
\(\large{ s = \frac{ a + b + c }{ 2 } }\) |
Where:
\(\large{ s }\) = semiperimeter
\(\large{ a,\; b, \;c }\) = edge
side of an Equilateral triangle formulas
\(\large{ a = \frac {P}{3} }\) | |
\(\large{ a = \frac{2}{3}\; 3^{3/4}\; \sqrt{A_{area}} }\) |
Where:
\(\large{ a, \;b, \;c }\) = edge
\(\large{ P }\) = perimeter
\(\large{ A_{area} }\) = area
Tags: Equations for Triangle