# 40 40 40 triangle

### Equilateral triangle.

Sides: a = 40   b = 40   c = 40

Area: T = 692.8220323028
Perimeter: p = 120
Semiperimeter: s = 60

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

Height: ha = 34.64110161514
Height: hb = 34.64110161514
Height: hc = 34.64110161514

Median: ma = 34.64110161514
Median: mb = 34.64110161514
Median: mc = 34.64110161514

Vertex coordinates: A[40; 0] B[0; 0] C[20; 34.64110161514]
Centroid: CG[20; 11.54770053838]
Coordinates of the circumscribed circle: U[20; 11.54770053838]
Coordinates of the inscribed circle: I[20; 11.54770053838]

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?

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. ### 1. The triangle circumference is the sum of the lengths of its three sides ### 2. Semiperimeter of the triangle ### 3. The triangle area using Heron's formula ### 4. Calculate the heights of the triangle from its area. ### 5. Calculation of the inner angles of the triangle using a Law of Cosines    