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 = 45.38770660042   b = 45.38770660042   c = 45.38770660042

Area: T = 892
Perimeter: p = 136.1611198013
Semiperimeter: s = 68.08105990063

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

Height: ha = 39.30663521629
Height: hb = 39.30663521629
Height: hc = 39.30663521629

Median: ma = 39.30663521629
Median: mb = 39.30663521629
Median: mc = 39.30663521629

Inradius: r = 13.10221173876
Circumradius: R = 26.20442347752

Vertex coordinates: A[45.38770660042; 0] B[0; 0] C[22.69435330021; 39.30663521629]
Centroid: CG[22.69435330021; 13.10221173876]
Coordinates of the circumscribed circle: U[22.69435330021; 13.10221173876]
Coordinates of the inscribed circle: I[22.69435330021; 13.10221173876]

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     