Triangle area = ½ × base × height

Dependencies: Parallelogram area = base × height.

Statement

In $\triangle ABC$, choose any side $BC$ as the base, with length $b$; from vertex $A$ drop a perpendicular foot $H$ onto line $BC$, and let $|AH|=h$ be the corresponding height. Then the area of the triangle is

Any of the three (base, height) pairs gives the same $S$ — the three base-times-height products are equal, a direct corollary of this formula.