Equilateral Triangle Calculator

Name: Equilateral Triangle - Geometry Calculator
Author: Jürgen Kummer

Calculations at an equilateral triangle or regular trigon. This is the most simple regular polygon (polygon with equal sides and angles).
Enter one value and choose the number of decimal places. Then click Calculate.

Formulas:

h = \sqrt{3} / 2 \cdot a

p = 3 \cdot a

A = a^{2} \cdot \sqrt{3} / 4

r_{c} = \sqrt{3} / 3 \cdot a

r_{i} = \sqrt{3} / 6 \cdot a

Angle: 60°
0 diagonals

Length, height, perimeter and radius have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).

Heights, bisecting lines, median lines, perpendicular bisectors and symmetry axes coincide. To these, the equilateral triangle is axially symmetric. They meet with centroid, circumcircle and incircle center in one point. To this, the equilateral triangle is rotationally symmetric at a rotation of 120°or multiples of this, so it has the order 3.

Equilateral triangle, perimeter and area

perimeter p, area A

heights h_a, h_b, h_c

incircle and circumcircle

angles and bisecting lines

median lines

perpendicular bisectors

The equilateral or regular triangle has three angles of 60 degrees each. The root of 3 appears in its height, incircle and circumference radius as well as the area, so all of these values are irrational. The equilateral triangle forms the sides of three of the five Platonic solids, these are tetrahedron, octahedron and icosahedron. With equilateral triangles, the plane can be tiled without any gaps, without creating a right angle at any point.
Regular polygons get closer and closer to a circle as the number of corners increases. The equilateral triangle has the fewest corners of all these polygons, so it can be understood as the regular shape that differs most from the circle. Since circular objects can roll and polygonal shapes roll better as the number of corners increases, shapes based on the equilateral triangle are the regular objects that resist rolling the most and therefore offer the best protection against unwanted rolling.

↑ up