Trapezoid Area Calculator (Trapezium)

Use $A = \frac{1}{2}(a + b) \times h$, where $a$ and $b$ are the two parallel sides (bases) and $h$ is the perpendicular height between them. The formula is the average of the two bases times the height.

If you place two identical trapezoids together (one flipped), they form a parallelogram with base $(a + b)$ and height $h$. The parallelogram has area $(a + b) \times h$, so each trapezoid is half that.

In American English, a trapezoid has exactly one pair of parallel sides. In British English, the same shape is called a trapezium. The formulas are identical — only the name differs by region.

Always use the perpendicular height — the shortest distance between the two parallel sides, measured at a right angle. The slant side is longer than the height and will give an incorrect (too large) result.

When $a = b$, the trapezoid becomes a parallelogram, and the formula simplifies to $A = a \times h$. When one side is zero ($a = 0$), the trapezoid degenerates into a triangle with $A = \frac{1}{2}bh$.