Equilateral triangle calculator (S)

Please enter one property of the equilateral triangle

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


You have entered area S.

Equilateral triangle.

Sides: a = 10.74656993182   b = 10.74656993182   c = 10.74656993182

Area: T = 50
Perimeter: p = 32.23770979547
Semiperimeter: s = 16.11985489774

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

Height: ha = 9.3066048591
Height: hb = 9.3066048591
Height: hc = 9.3066048591

Median: ma = 9.3066048591
Median: mb = 9.3066048591
Median: mc = 9.3066048591

Inradius: r = 3.1022016197
Circumradius: R = 6.2044032394

Vertex coordinates: A[10.74656993182; 0] B[0; 0] C[5.37328496591; 9.3066048591]
Centroid: CG[5.37328496591; 3.1022016197]
Coordinates of the circumscribed circle: U[5.37328496591; 3.1022016197]
Coordinates of the inscribed circle: I[5.37328496591; 3.1022016197]

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: area S

S = 50 ; ;

2. From area S we calculate side a:

a = 4 S / sqrt{ 3 } = 4 * 50 / sqrt{ 3 } = 10.746 ; ;

3. From side a we calculate b,c:

b = c = a = 10.746 ; ;


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 = 10.75 ; ; b = 10.75 ; ; c = 10.75 ; ;

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

p = a+b+c = 10.75+10.75+10.75 = 32.24 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 32.24 }{ 2 } = 16.12 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16.12 * (16.12-10.75)(16.12-10.75)(16.12-10.75) } ; ; T = sqrt{ 2500 } = 50 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 50 }{ 10.75 } = 9.31 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 50 }{ 10.75 } = 9.31 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 50 }{ 10.75 } = 9.31 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 10.75**2-10.75**2-10.75**2 }{ 2 * 10.75 * 10.75 } ) = 60° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 10.75**2-10.75**2-10.75**2 }{ 2 * 10.75 * 10.75 } ) = 60° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 10.75**2-10.75**2-10.75**2 }{ 2 * 10.75 * 10.75 } ) = 60° ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 50 }{ 16.12 } = 3.1 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10.75 }{ 2 * sin 60° } = 6.2 ; ;




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