Heron's Formula

Triangle area from its three side lengths.

A = s (s - a) (s - b) (s - c), s = \frac{a + b + c}{2}

Variables

Useful when no height is known. If the value under the root is negative, the sides cannot form a triangle.

Sides 3, 4, 5: $s = 6$ , $A = 6 \cdot 3 \cdot 2 \cdot 1 = 6$ .

Solve any triangle from SSS, SAS or ASA: all sides, angles, area, perimeter and type using the laws of sines and cosines.

Area of a Triangle

Half of base times height.