Parallelogram area = base × height

Dependencies: SAS congruence; the area axioms (region additivity + invariance under congruence + unit square ⇒ rectangle area = length × width).

Statement

Let parallelogram $ABCD$ have one pair of opposite sides $AB \parallel CD$ designated as the base, with length $b = |AB| = |CD|$; taking the line $AB$ containing the base as reference, let the distance from the opposite side $CD$ to $AB$ (i.e. the perpendicular distance from any point on $CD$ to the line $AB$) be the height $h$. Then the area of parallelogram $ABCD$ is