# 12 12 14 triangle

### Acute isosceles triangle.

Sides: a = 12   b = 12   c = 14

Area: T = 68.22875604137
Perimeter: p = 38
Semiperimeter: s = 19

Angle ∠ A = α = 54.31546652873° = 54°18'53″ = 0.94879697414 rad
Angle ∠ B = β = 54.31546652873° = 54°18'53″ = 0.94879697414 rad
Angle ∠ C = γ = 71.37106694253° = 71°22'14″ = 1.24656531708 rad

Height: ha = 11.37112600689
Height: hb = 11.37112600689
Height: hc = 9.74767943448

Median: ma = 11.57658369028
Median: mb = 11.57658369028
Median: mc = 9.74767943448

Inradius: r = 3.59109242323
Circumradius: R = 7.3877044135

Vertex coordinates: A[14; 0] B[0; 0] C[7; 9.74767943448]
Centroid: CG[7; 3.24989314483]
Coordinates of the circumscribed circle: U[7; 2.36597502098]
Coordinates of the inscribed circle: I[7; 3.59109242323]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.6855334713° = 125°41'7″ = 0.94879697414 rad
∠ B' = β' = 125.6855334713° = 125°41'7″ = 0.94879697414 rad
∠ C' = γ' = 108.6299330575° = 108°37'46″ = 1.24656531708 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    