Triangle Formulas

1. Area of Triangle Formula

Area = \frac{Base \times Height}{2}

Area is half the product of base and height.

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

Uses side lengths a, b, c and semi-perimeter s = $\frac{a + b + c}{2}$ .

c^{2} = a^{2} + b^{2}

In a right triangle, c is the hypotenuse.

R = \frac{abc}{4 \times Area}

Circumradius R depends on sides a, b, c and area.

r = \frac{Area}{s}

Inradius r is area divided by semi-perimeter s.

\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}

Relates sides and angles of a triangle.

c^{2} = a^{2} + b^{2} - 2 a b cos C

Used to calculate sides or angles in any triangle.

Area = \frac{1 \times 2 a b sin C}{1}

For known two sides a, b and included angle C.