Equilateral triangle Equilateral triangle In geometry, an equilateral triangle is a triangle in which all three sides are equal. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°. It is also a regular polygon, so it is also referred to as a regular triangle. Denoting the common length of the sides of the equilateral triangle as "a", we can determine using the Pythagorean theorem that: Denoting the radius of the circumscribed circle as "R", we can determine using trigonometry that: Many of these quantities
Triangle (in fact, this formula holds for "all" tangential polygons), and where formula_59 are the radii of the excircles tangent to sides "a, b, c" respectively. We also have and for circumdiameter "D"; and for angle α ≠ 90°. The area can also be expressed as In 1885, Baker gave a collection of over a hundred distinct area formulas for the triangle. These include: for circumradius (radius of the circumcircle) "R", and The area "T" of any triangle with perimeter "p" satisfies with equality holding if and only if the triangle is equilateral. Other upper bounds on the area "T" are