Triangle Formulas

Angles and sides

Angle sum

∠ A + ∠ B + ∠ C = 180^{\circ}

Exterior angle

exterior angle = sum of the two remote interior angles

Triangle inequality

| a - b | < c < a + b

Base and height

A = \frac{1}{2} b h

Heron's formula

A = \sqrt{s (s - a) (s - b) (s - c)}

s = (a + b + c)/2

Equilateral triangle

A = \frac{\sqrt{3}}{4} s^{2}

height (√3/2)s

From the inradius

A = r s

r inradius, s semiperimeter

From the circumradius

A = \frac{a b c}{4 R}

R circumradius

From coordinates

A = \frac{1}{2} | x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2}) |

Centroid

G = (\frac{x_{1} + x_{2} + x_{3}}{3}, \frac{y_{1} + y_{2} + y_{3}}{3})

divides each median 2 : 1

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