Equilateral triangle

Equilateral triangle

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.

Video: What is an equilateral triangle

Principal properties

An equilateral triangle. It has equal sides (a=b=c), equal angles (), and equal altitudes (h_a=h_b=h_c).

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 
• The geometric center of the triangle is the center of the circumscribed and inscribed circles
• And the altitude (height) from any side is .

Denoting the radius of the circumscribed circle as R, we can determine using trigonometry that:

• The area of the triangle 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, or apothem, is 
• The radius of the circle circumscribing the three vertices is 
• The radius of the inscribed circle is 

In an equilateral triangle, the altitudes, the angle bisectors, the ......

‹ Ellipse video          up           Equilateral triangle video ›