Equilateral triangle

In geometry, an equilateral triangle is a triangle in which all three sides are equal. In the familiar Euclidean geometry, equilateral triangles are also equiangular; that is, all three internal angles are also congruent to each other and are each 60°. They are regular polygons, and can therefore also be referred to as regular triangles.

Principal properties

Denoting the common length of the sides of the equilateral triangle as a, we can determine using the Pythagorean theorem that:

The area is

The perimeter is

The radius of the circumscribed circle is

The radius of the inscribed circle is or

And the altitude (height) from any side is .

Many of these quantities have simple relationships to the altitude ("h") of each vertex from the opposite side:

The area is

The height of the center from each side is

The radius of the circle circumscribing the three vertices is

The radius of the inscribed circle is

Equilateral (disambiguation)

Equilateral can refer to:

See also