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A standard yield road sign is an equilateral triangle with sides of approximately 75 cm.
Key values: side = 75 cm · area ≈ 2,437 cm² · height ≈ 64.95 cm
A 2 m equilateral triangular steel frame for a structural brace.
Key values: side = 2 m · area ≈ 1.732 m² · perimeter = 6 m
Select your known values (SSS, SAS, ASA, AAS, or SSA) and enter measurements to solve the triangle and compute area, perimeter, inradius, and more.
An equilateral triangle has all three sides equal and all three angles equal to 60°. It is the simplest regular polygon and the only triangle where every center point (centroid, circumcenter, incenter, orthocenter) coincides.
Every equilateral triangle is determined by a single measurement: the side length . All other properties follow from it.
Given side length :
Height (altitude)
Derived from the 30-60-90 triangle formed by dropping an altitude.
Area
From .
Perimeter
Circumradius (circumscribed circle)
Inradius (inscribed circle)
The inradius is exactly half the circumradius: .
Drop an altitude from any vertex to the opposite side. This bisects the base, creating two 30-60-90 right triangles with legs and , and hypotenuse :
The factor is the ratio of height to side. Every equilateral triangle formula derives from this single geometric fact.
The equilateral triangle is one of only three regular polygons that tile the plane (along with the square and regular hexagon). Six equilateral triangles meet at each vertex because .
Connection to hexagons: A regular hexagon is made of exactly 6 equilateral triangles. The area of a regular hexagon with side is therefore .
An equilateral triangle has all three sides equal in length and all three interior angles equal to . It is the simplest regular polygon, and every center point (centroid, circumcenter, incenter, orthocenter) coincides at the same location.
Given side length , the area is . This is derived from the base-height formula , where the height comes from the 30-60-90 triangle formed by dropping an altitude.
The height (altitude) of an equilateral triangle with side is . This is derived from the Pythagorean theorem applied to the 30-60-90 right triangle formed when an altitude bisects the base.
In an equilateral triangle, the inradius is exactly half the circumradius: . The circumradius is and the inradius is , where is the side length.
Equilateral triangles tile the plane because six of them fit perfectly around a single vertex: . They are one of only three regular polygons that can tessellate the plane, along with squares and regular hexagons.