Finding the Height of a Trapezoid
The height (or altitude) of a trapezoid is the perpendicular distance between its two parallel sides. There are several ways to determine this value depending on what information is available.
Methods to Find Height
From Area and Parallel Sides
Rearranging the area formula A = ½(a + b)h gives the height directly.
h = 2A / (a + b)
From Leg and Base Angle
Using trigonometry, the height is the leg times the sine of the base angle.
h = leg x sin(angle)
From Leg and Sides (Pythagorean)
If you know a leg and the horizontal offset, use the Pythagorean theorem.
h = sqrt(leg^2 - offset^2)
When to Use Each Method
- Area method: Best when you already know the area and both parallel sides. This is the most direct rearrangement.
- Leg-angle method: Useful when a leg length and one base angle are measured, common in surveying.
- Pythagorean method: Applied when legs and base difference are known, particularly for isosceles trapezoids.
Important Notes
- Height is always perpendicular to the parallel sides, not along the leg.
- The leg length is always greater than or equal to the height.
- For a right trapezoid, one leg equals the height.