Equilateral triangle calculator - result

Please enter one property of the equilateral triangle

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


You have entered perimeter p.

Equilateral triangle.

Sides: a = 24   b = 24   c = 24

Area: T = 249.415531629
Perimeter: p = 72
Semiperimeter: s = 36

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

Height: ha = 20.78546096908
Height: hb = 20.78546096908
Height: hc = 20.78546096908

Median: ma = 20.78546096908
Median: mb = 20.78546096908
Median: mc = 20.78546096908

Inradius: r = 6.92882032303
Circumradius: R = 13.85664064606

Vertex coordinates: A[24; 0] B[0; 0] C[12; 20.78546096908]
Centroid: CG[12; 6.92882032303]
Coordinates of the circumscribed circle: U[12; 6.92882032303]
Coordinates of the inscribed circle: I[12; 6.92882032303]

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

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How did we calculate this triangle?

1. Input data entered: perimeter p

p = 72 ; ;

2. From perimeter p we calculate side a:

a = p / 3 = 72/3 = 24 ; ;

3. From side a we calculate b,c:

b = c = a = 24 ; ;


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 = 24 ; ; b = 24 ; ; c = 24 ; ;

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

p = a+b+c = 24+24+24 = 72 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 72 }{ 2 } = 36 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36 * (36-24)(36-24)(36-24) } ; ; T = sqrt{ 62208 } = 249.42 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 249.42 }{ 24 } = 20.78 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 249.42 }{ 24 } = 20.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 249.42 }{ 24 } = 20.78 ; ;

8. 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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 24**2+24**2-24**2 }{ 2 * 24 * 24 } ) = 60° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 24**2+24**2-24**2 }{ 2 * 24 * 24 } ) = 60° ; ; gamma = 180° - alpha - beta = 180° - 60° - 60° = 60° ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 249.42 }{ 36 } = 6.93 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 24 }{ 2 * sin 60° } = 13.86 ; ;

11. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 24**2 - 24**2 } }{ 2 } = 20.785 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 24**2 - 24**2 } }{ 2 } = 20.785 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 24**2 - 24**2 } }{ 2 } = 20.785 ; ;
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