Area of a triangle

In geometry, calculating the area of a triangle is an elementary and widely encountered problem. The best known and simplest formula for the area of an arbitrary triangle is $${\displaystyle {\text{area}}={\tfrac {1}{2}}\times {\text{base}}\times {\text{height}},}$$ where "base" means the length of any side of the triangle, and "height" means the shortest distance between the line of the base and the corresponding apex (opposite corner of the triangle).

Although simple, this formula is only useful if the height can be readily found, which is not always the case. For example, the land surveyor of a triangular field might find it relatively easy to measure the length of each side, but relatively difficult to construct a 'height'. Various methods may be used in practice, depending on what is known about the triangle. Other frequently used formulas for the area of a triangle use trigonometry, side lengths (Heron's formula), vectors, coordinates, line integrals, Pick's theorem, or other properties.