Trapezoid area = ½ × (a + b) × h

Dependencies: Triangle area = ½ × base × height.

Statement

Let trapezoid $ABCD$ have parallel sides $AB$ and $CD$ (i.e. $AB \parallel CD$): top side $|AB|=a$, bottom side $|CD|=b$, and distance between the two parallel sides (the height) $h$. Then the area of the trapezoid is

In words, "half the sum of the two parallel sides" times "height" is the trapezoid's area. When $a=b$ this degenerates to a parallelogram ($S=bh$); when $a=0$ it degenerates to a triangle ($S=\tfrac{1}{2}bh$); the formula thus unifies the area of a whole family of figures into a single expression.