Trapezoid Formulas
Median (m) = (a + b) / 2
Area = m × h
Perimeter = a + b + c + d
Where a and b are the two parallel bases, h is the perpendicular height, c and d are the non-parallel sides (legs), and m is the median (midline).
Example
Trapezoid with bases 8 cm and 5 cm, height 4 cm
Area = ½ × (8 + 5) × 4 = ½ × 13 × 4 = 26 cm²
Median = (8 + 5) / 2 = 6.5 cm
Types of Trapezoids
| Type | Description |
|---|---|
| Right trapezoid | One leg is perpendicular to the bases (one right angle) |
| Isosceles trapezoid | Both legs are equal in length; base angles are equal |
| Scalene trapezoid | No special symmetry; all sides different |
| Parallelogram | Special case: both pairs of sides are parallel (a = b would make it a rectangle) |
Frequently Asked Questions
What is the difference between a trapezoid and a trapezium?
In North America (US/Canada), a trapezoid has exactly one pair of parallel sides. In the UK and much of the world, this same shape is called a trapezium. The terms refer to the same shape — just different regional conventions.
Why does the formula use the average of the two bases?
The trapezoid area formula ½×(a+b)×h comes from averaging the two base lengths to find the "average width," then multiplying by height. You can also see this as the area of a rectangle with width = median and height = h.
What if the trapezoid has legs of different lengths?
The area formula only requires the two parallel bases and the height — the leg lengths don't affect the area. However, you need all four sides for the perimeter. The optional leg fields in this calculator let you find the perimeter when you know those measurements.