Equilateral triangle calculator

Please enter one property of the equilateral triangle

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

You have entered side a, b and c (as equilateral triangle).

Equilateral triangle.

Sides: a = 45   b = 45   c = 45

Area: T = 876.8510721332
Perimeter: p = 135
Semiperimeter: s = 67.5

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

Height: ha = 38.97111431703
Height: hb = 38.97111431703
Height: hc = 38.97111431703

Median: ma = 38.97111431703
Median: mb = 38.97111431703
Median: mc = 38.97111431703

Inradius: r = 12.99903810568
Circumradius: R = 25.98107621135

Vertex coordinates: A[45; 0] B[0; 0] C[22.5; 38.97111431703]
Centroid: CG[22.5; 12.99903810568]
Coordinates of the circumscribed circle: U[22.5; 12.99903810568]
Coordinates of the inscribed circle: I[22.5; 12.99903810568]

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: side a, b and c (as equilateral triangle) 2. From 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. 3. The triangle circumference is the sum of the lengths of its three sides 4. Semiperimeter of the triangle 5. The triangle area using Heron's formula 6. Calculate the heights of the triangle from its area. 7. Calculation of the inner angles of the triangle using a Law of Cosines    