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 = 4   b = 4   c = 4

Area: T = 6.92882032303
Perimeter: p = 12
Semiperimeter: s = 6

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

Height: ha = 3.46441016151
Height: hb = 3.46441016151
Height: hc = 3.46441016151

Median: ma = 3.46441016151
Median: mb = 3.46441016151
Median: mc = 3.46441016151

Inradius: r = 1.15547005384
Circumradius: R = 2.30994010768

Vertex coordinates: A[4; 0] B[0; 0] C[2; 3.46441016151]
Centroid: CG[2; 1.15547005384]
Coordinates of the circumscribed circle: U[2; 1.15547005384]
Coordinates of the inscribed circle: I[2; 1.15547005384]

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 = 4 ; ;

2. From side a we calculate b,c:

b = c = a = 4 ; ;


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 = 4 ; ; b = 4 ; ; c = 4 ; ;

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

p = a+b+c = 4+4+4 = 12 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 12 }{ 2 } = 6 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6 * (6-4)(6-4)(6-4) } ; ; T = sqrt{ 48 } = 6.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6.93 }{ 4 } = 3.46 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6.93 }{ 4 } = 3.46 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6.93 }{ 4 } = 3.46 ; ;

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{ 4**2-4**2-4**2 }{ 2 * 4 * 4 } ) = 60° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4**2-4**2-4**2 }{ 2 * 4 * 4 } ) = 60° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 4**2-4**2-4**2 }{ 2 * 4 * 4 } ) = 60° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6.93 }{ 6 } = 1.15 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 60° } = 2.31 ; ;




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