Trapezoid Height Calculator
Determine the altitude of any trapezoid using Area, Sides, or Angles. Supports Isosceles, Right, and Scalene trapezoids with distinct calculation methods.
Height: --
About
A trapezoid (or trapezium in UK English) is a quadrilateral with at least one pair of parallel sides. The distance between these two parallel bases is the height (altitude). Knowing the height is essential for determining area and structural stability in architecture.
This tool solves for height using three different known states: 1) Known Area and Bases, 2) Known Sides (using a complex trigonometric derivation), or 3) Trigonometry with angles. It handles the complexity of general scalene trapezoids automatically.
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Formulas
For the basic Area method:
h = 2 Aa + b
Where a and b are the parallel bases.
Reference Data
| Given Variables | Formula for Height (h) |
|---|---|
| Area (A), Bases (a, b) | h = 2Aa + b |
| Side (c), Angle (α) | h = c ⋅ sin(α) |
| All 4 Sides | (Uses Heron's formula on the triangle formed by sliding legs together) |
Frequently Asked Questions
You can still find the height! Imagine sliding the two non-parallel legs together to form a triangle with the base equal to the difference of the parallel sides. This tool performs that calculation automatically.
Only in a Right Trapezoid, where one of the non-parallel sides is perpendicular to the bases. In all other cases, the height is shorter than the slanted sides.