Equilateral triangle calculator (a)

Please enter one property of the equilateral triangle

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


You have entered side a.

Equilateral triangle.

Sides: a = 6   b = 6   c = 6

Area: T = 15.58884572681
Perimeter: p = 18
Semiperimeter: s = 9

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

Height: ha = 5.19661524227
Height: hb = 5.19661524227
Height: hc = 5.19661524227

Median: ma = 5.19661524227
Median: mb = 5.19661524227
Median: mc = 5.19661524227

Inradius: r = 1.73220508076
Circumradius: R = 3.46441016151

Vertex coordinates: A[6; 0] B[0; 0] C[3; 5.19661524227]
Centroid: CG[3; 1.73220508076]
Coordinates of the circumscribed circle: U[3; 1.73220508076]
Coordinates of the inscribed circle: I[3; 1.73220508076]

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: side a

a = 6 ; ;

2. From side a we calculate b,c:

b = c = a = 6 ; ;


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 = 6 ; ; b = 6 ; ; c = 6 ; ;

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

p = a+b+c = 6+6+6 = 18 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 18 }{ 2 } = 9 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 9 * (9-6)(9-6)(9-6) } ; ; T = sqrt{ 243 } = 15.59 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 15.59 }{ 6 } = 5.2 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 15.59 }{ 6 } = 5.2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 15.59 }{ 6 } = 5.2 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 6**2+6**2-6**2 }{ 2 * 6 * 6 } ) = 60° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6**2+6**2-6**2 }{ 2 * 6 * 6 } ) = 60° ; ; gamma = 180° - alpha - beta = 180° - 60° - 60° = 60° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 15.59 }{ 9 } = 1.73 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6 }{ 2 * sin 60° } = 3.46 ; ;

10. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 6**2+2 * 6**2 - 6**2 } }{ 2 } = 5.196 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6**2+2 * 6**2 - 6**2 } }{ 2 } = 5.196 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 6**2+2 * 6**2 - 6**2 } }{ 2 } = 5.196 ; ;
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