Trapezoid Height Calculator

Enter a trapezoid's area and the lengths of its two parallel sides (bases) to find its height using h = 2A / (b₁ + b₂), plus the median (midsegment) length and base difference.

Quick Facts

Area formula
A = ½(b₁ + b₂)h
The standard trapezoid area formula, using the two parallel sides (bases) and the height.
Height formula
h = 2A / (b₁ + b₂)
Rearranging the area formula to solve for height instead of area.
Median shortcut
h = A / m, where m = (b₁ + b₂) / 2
The median (midsegment) is the average of the two bases; height equals area divided by the median.

Your Results

Calculated
Height
-
h = 2A / (b₁ + b₂)
Median (Midsegment)
-
m = (b₁ + b₂) / 2
Sum of Bases
-
b₁ + b₂
Base Difference
-
|b₁ − b₂|

Ready

Enter the area and both base lengths, then press Calculate.

Formula and Method for Trapezoid Height

A trapezoid (or trapezium) is a quadrilateral with exactly one pair of parallel sides, called the bases (b₁ and b₂). Its area is A = ½(b₁ + b₂)h, where h is the perpendicular distance between the two bases. This calculator rearranges that formula to solve for height directly: h = 2A / (b₁ + b₂), given the area and the lengths of both bases.

How the calculation works

Enter the trapezoid's area and the lengths of its two parallel sides in the same unit system — the area should be in that unit squared (e.g., ft² if the bases are in feet). The calculator doubles the area and divides by the sum of the bases to isolate the height: h = 2A / (b₁ + b₂). It also reports the median (midsegment) m = (b₁ + b₂) / 2 — the segment connecting the midpoints of the two legs, whose length is the average of the bases. Because area equals median times height (A = m × h), height can equivalently be found as h = A / m.

Common mistakes

  • Using the legs instead of the bases: b₁ and b₂ must be the two parallel sides. The non-parallel sides (legs) do not appear in this formula.
  • Mixing units: area must be expressed in the same unit² as the bases you enter — for example, use ft² with feet, not m² with feet.
  • Forgetting the factor of 2: height equals 2A divided by the sum of the bases, not A divided by the sum — omitting the 2 halves the correct answer.

Real-world applications

  • Civil engineering and surveying use trapezoid height to compute cross-sectional areas of canals, roads, and embankments.
  • Architecture and carpentry use it to size trapezoidal panels, roof sections, and countertops from a known area.
  • Land surveying applies the related trapezoidal rule to estimate irregular plot areas from parallel offset measurements.
  • Geometry students commonly solve for height when given the area and bases as the unknown variable in a word problem.

Frequently Asked Questions

What is the formula for trapezoid height?
Rearranging the trapezoid area formula A = ½(b₁ + b₂)h gives h = 2A / (b₁ + b₂), where A is the area and b₁, b₂ are the lengths of the two parallel sides (bases).
How does the median (midsegment) relate to trapezoid height?
The median m is the average of the two bases, m = (b₁ + b₂) / 2. Since area equals median times height (A = m × h), height can also be found as h = A / m.
Can I find the height from the four side lengths instead of the area?
Yes. If you know both bases (b₁, b₂) and both legs (c, d), let x = [c² − d² + (b₁ − b₂)²] / [2(b₁ − b₂)], then the height is h = √(c² − x²). This comes from splitting the trapezoid into a rectangle and two right triangles.
What happens when the two bases are equal?
If b₁ = b₂, the shape becomes a parallelogram (or rectangle) and the height simplifies to h = A / b, since the median equals the common base length.

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