

$$2p = S \times 3$$
Perimeter
$$A = \frac{S \times h}{2}$$
Area
$$S = \frac{A \times 2}{h}$$
$$h = \frac{A \times 2}{S}$$
$$S = \frac{2p}{3}$$
Side
Knowing side or height only
$$2p = 2 h \sqrt{3}$$
Perimeter (with height)
$$h = \frac{2p}{2\sqrt{3}}$$
Height (from perimeter)
$$A = \frac{\sqrt{3}}{4} {S}^2$$
Area (with side)
$$A = \frac{{h}^2}{\sqrt{3}}$$
Area (with height)
$$S = \frac{2h}{\sqrt{3}}$$
Side (with height)
$$h = \frac{S\sqrt{3}}{2}$$
Height (with side)
Inscribed circumference
$$r = \frac{1}{2 \sqrt{3}} S$$
Inscribed radius (with side)
$$r = \frac{1}{3} h$$
Inscribed radius (with height)
$$S = 2r\sqrt{3}$$
Side
$$h = 3r$$
Height
$$2p = 6r\sqrt{3}$$
Perimeter
$$A = 3{r}^2 \sqrt{3}$$
Area
Circumscribed circumference
$$R = \frac{\sqrt{3}}{3} S$$
Circumscribed radius (with side)
$$R = \frac{2}{3} h$$
Circumscribed radius (with side)
$$S = R\sqrt{3}$$
Side
$$h = \frac{3}{2}R$$
Height
$$2p = 3\sqrt{3}R$$
Perimeter
$$A = \frac{3\sqrt{3}}{4}{R}^2$$
Area
Definition
An equilateral triangle is a triangle with all sides congruent.
Properties
 All sides are congruent
 All angles are congruent
 All the Generic Triangle formulas are valid
 The height relative to the base divides the shape in two congruent right triangles. For these are valid the Right Triangle formulas
Equilateral Triangle Formulas
Data  Formula 

Perimeter  2p = S × 3 
Area  A = (S × h) / 2 
Side  S = 2p / 3 
Side (with height)  S = (2 × h) / √3 
Height (with side)  h = (S√3) / 2 
Height (from perimeter)  h = 2p / (2√3) 
Perimeter (with height)  A = 2 × h × √3 
Area (with side)  A = (√3 / 4) × S^{2} 
Area (with height)  A = h^{2} / √3 
Side  S = (A × 2) / h 
Height  h = (A × 2) / S 
Equilateral Triangle  Inscribed circumference
Data  Formula 

Inscribed radius (with side)  r = [1 / (2√3)] × S 
Inscribed radius (with height)  r = 1/3 × h 
Side  S = 2r√3 
Height  h = 3r 
Perimeter  2p = 6r√3 
Area  A = 3r^{2}√3 
Equilateral Triangle  Circumscribed circumference
Data  Formula 

Circumscribed radius (with side)  r = (√3 / 3) × S 
Circumscribed radius (with height)  r = 2/3 × h 
Side  S = R√3 
Height  h = 3/2 × R 
Perimeter  2p = 3√3R 
Area  A = [(3√3) / 4] × R^{2} 