Trapezoid Height Calculator — Find h from Area or Leg
Find the perpendicular height of a trapezoid — either from its area and two bases (h = 2A/(a+b)), or from the leg length of an isosceles trapezoid using the Pythagorean theorem.
Find height from
Perpendicular distance between the two parallel bases: h = 2A / (a + b)
- 1
Sum of parallel bases
a + b = 6 + 10 = 16 - 2
Double the area
2 × 64 = 128 - 3
Height h = 2A ÷ (a + b)
128 ÷ 16 = 8
How does this calculator work?
Trapezoid height from area: h = 2A/(a+b). From leg (isosceles): h = √(c²−((b−a)/2)²). The height is always perpendicular to the two parallel bases, not the slant leg length. Use the area method when the area is known; use the leg method for isosceles trapezoids.
Formula
How this is calculated
The height of a trapezoid is the perpendicular (shortest) distance between its two parallel sides (bases). It appears in the area formula A = (a + b) / 2 × h, so if you already know the area, rearranging gives h = 2A / (a + b). This is the most direct route when the area is given — no trigonometry needed.
For an isosceles trapezoid (equal legs), you can derive the height geometrically. Dropping perpendiculars from the top corners to the bottom base creates two congruent right triangles, each with hypotenuse c (the leg) and base (b−a)/2. The Pythagorean theorem then gives h = √(c² − ((b−a)/2)²). The area follows as A = (a+b)/2 × h.
Both methods assume the height is the internal perpendicular distance, not the slant length of the leg. For a right trapezoid (one leg perpendicular to the bases) the height equals the perpendicular leg directly. This calculator handles the common isosceles case; for a general scalene trapezoid you would need to know both leg lengths or one leg and one base angle.
Frequently asked questions
The height (altitude) is the perpendicular distance between the two parallel bases — it is always measured at a right angle. The leg is the slant side connecting a top corner to a bottom corner; it equals the height only in a right trapezoid where one leg is vertical.
Yes — for a right trapezoid, choose "leg length" mode and set the leg equal to the perpendicular side (the right-angle leg). Since the offset = (b−a)/2 may not match, it is easier to use the "from area" method, or simply read the perpendicular leg directly as the height.
Rearrange the area formula: A = (a + b) / 2 × h. The trapezoid-area calculator on this platform does this directly.
Also known as
TG we-Calculate Editorial Team. (2026). Trapezoid Height Calculator — Find h from Area or Leg [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/trapezoid-height-calculator
TG we-Calculate Editorial Team. "Trapezoid Height Calculator — Find h from Area or Leg." TG we-Calculate. 2026. https://we-calculate.com/calculator/trapezoid-height-calculator.
TG we-Calculate Editorial Team, "Trapezoid Height Calculator — Find h from Area or Leg," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/trapezoid-height-calculator
@misc{wecalculate_trapezoid_height_calculator, title = {Trapezoid Height Calculator — Find h from Area or Leg}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/trapezoid-height-calculator}}, year = {2026}, note = {TG we-Calculate} }
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