Equilateral triangle calculator (S)

Please enter one property of the equilateral triangle

Use symbols: a, h, T, p, r, R

You have entered area S.

Equilateral triangle.

Sides: a = 10.74656993182   b = 10.74656993182   c = 10.74656993182

Area: T = 50
Perimeter: p = 32.23770979547
Semiperimeter: s = 16.11985489774

Angle ∠ A = α = 60° = 1.04771975512 rad
Angle ∠ B = β = 60° = 1.04771975512 rad
Angle ∠ C = γ = 60° = 1.04771975512 rad

Height: ha = 9.3066048591
Height: hb = 9.3066048591
Height: hc = 9.3066048591

Median: ma = 9.3066048591
Median: mb = 9.3066048591
Median: mc = 9.3066048591

Inradius: r = 3.1022016197
Circumradius: R = 6.2044032394

Vertex coordinates: A[10.74656993182; 0] B[0; 0] C[5.37328496591; 9.3066048591]
Centroid: CG[5.37328496591; 3.1022016197]
Coordinates of the circumscribed circle: U[5.37328496591; 3.1022016197]
Coordinates of the inscribed circle: I[5.37328496591; 3.1022016197]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 120° = 1.04771975512 rad
∠ B' = β' = 120° = 1.04771975512 rad
∠ C' = γ' = 120° = 1.04771975512 rad

How did we calculate this triangle?

1. Input data entered: area S 2. From area S we calculate side a: 3. From side a we calculate b,c: Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS. 4. The triangle circumference is the sum of the lengths of its three sides 5. Semiperimeter of the triangle 6. The triangle area using Heron's formula 7. Calculate the heights of the triangle from its area. 8. Calculation of the inner angles of the triangle using a Law of Cosines     