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 = 7.1   b = 7.1   c = 7.1

Area: T = 21.82881703024
Perimeter: p = 21.3
Semiperimeter: s = 10.65

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

Height: ha = 6.14987803669
Height: hb = 6.14987803669
Height: hc = 6.14987803669

Median: ma = 6.14987803669
Median: mb = 6.14987803669
Median: mc = 6.14987803669

Inradius: r = 2.05495934556
Circumradius: R = 4.09991869112

Vertex coordinates: A[7.1; 0] B[0; 0] C[3.55; 6.14987803669]
Centroid: CG[3.55; 2.05495934556]
Coordinates of the circumscribed circle: U[3.55; 2.05495934556]
Coordinates of the inscribed circle: I[3.55; 2.05495934556]

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

Calculate another triangle




How did we calculate this triangle?

1. Input data entered: side a b c (as equilateral triangle)

a = 7.1 ; ; b = 7.1 ; ; c = 7.1 ; ;

2. From we calculate b,c:

b = c = a = 7.1 ; ;


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.

a = 7.1 ; ; b = 7.1 ; ; c = 7.1 ; ; : Nr. 1

3. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 7.1+7.1+7.1 = 21.3 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 21.3 }{ 2 } = 10.65 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 10.65 * (10.65-7.1)(10.65-7.1)(10.65-7.1) } ; ; T = sqrt{ 476.47 } = 21.83 ; ;

6. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 21.83 }{ 7.1 } = 6.15 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 21.83 }{ 7.1 } = 6.15 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 21.83 }{ 7.1 } = 6.15 ; ;

7. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 7.1**2-7.1**2-7.1**2 }{ 2 * 7.1 * 7.1 } ) = 60° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7.1**2-7.1**2-7.1**2 }{ 2 * 7.1 * 7.1 } ) = 60° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 7.1**2-7.1**2-7.1**2 }{ 2 * 7.1 * 7.1 } ) = 60° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 21.83 }{ 10.65 } = 2.05 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7.1 }{ 2 * sin 60° } = 4.1 ; ;




Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.