# 21 21 21 triangle

### Equilateral triangle.

Sides: a = 21   b = 21   c = 21

Area: T = 190.9598601534
Perimeter: p = 63
Semiperimeter: s = 31.5

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

Height: ha = 18.18765334795
Height: hb = 18.18765334795
Height: hc = 18.18765334795

Median: ma = 18.18765334795
Median: mb = 18.18765334795
Median: mc = 18.18765334795

Inradius: r = 6.06221778265
Circumradius: R = 12.1244355653

Vertex coordinates: A[21; 0] B[0; 0] C[10.5; 18.18765334795]
Centroid: CG[10.5; 6.06221778265]
Coordinates of the circumscribed circle: U[10.5; 6.06221778265]
Coordinates of the inscribed circle: I[10.5; 6.06221778265]

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    