SamCalculator

Trapezoid Area Calculator

Calculate trapezoid area, median (midsegment) length, height, and area conversions using the parallel-bases formula.

Choose a shape

Trapezoid inputs

A = ½(b₁ + b₂) × h
m
m
m

Master area formula library

Rectangle

A = l × w

Length times width.

Square

A = s²

A rectangle with equal sides.

Triangle

A = ½ × b × h

Half the base times the height.

Triangle (Heron)

A = √[s(s−a)(s−b)(s−c)]

From three side lengths only.

Trapezoid

A = ½(b₁ + b₂) × h

Average of the parallel bases × height.

Circle

A = π × r²

Pi times the radius squared.

Sector

A = ½ × r² × θ

Radians for θ.

Ellipse

A = π × a × b

Semi-major × semi-minor × π.

Parallelogram

A = b × h

Base times perpendicular height.

Rhombus

A = ½ × d₁ × d₂

Half the product of the diagonals.

Kite

A = ½ × d₁ × d₂

Same as the rhombus diagonal rule.

Regular polygon

A = ½ × n × s × a

n sides of length s, apothem a.

Polygon

A = ½ |Σ(xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ)|

Shoelace / Surveyor's formula.

Related geometry calculators

Circle CalculatorRadius, diameter, circumference, arc, chord, segment.Triangle CalculatorRight, isosceles, equilateral, area, and angle solvers.Distance Calculator2D, 3D, lat/lon, vector, and map distance.Scientific CalculatorTrig, exponents, roots, logs, and constants.Slope CalculatorSlope, midpoint, intercepts, and line equations.Unit ConverterLength, area, volume, and 40+ measurement categories.

What Is the Trapezoid Area Formula?

Trapezoid area calculations let you find the two-dimensional extent of a trapezoid from its defining measurements. The formula A = ½(b₁ + b₂) × h captures the relationship between the inputs and the area; the calculator applies it instantly, returns a full unit-conversion panel, and shows every substitution step.

The formula used on this page is A = ½(b₁ + b₂) × h. The calculator applies it instantly, returns full unit conversions, and shows every substitution in the step-by-step panel.

How the Calculation Works

The trapezoid area formula A = ½(b₁ + b₂) × h comes from classical Euclidean geometry. The inputs you enter are substituted directly into the formula; the result is the area in the square of your input unit. The step-by-step panel below the result mirrors how the same calculation would be written on paper.

6 Ways to Use This Trapezoid Calculator

1

Geometry coursework

Solve textbook trapezoid area problems and see the full step-by-step working alongside the final answer.

2

Practical sizing

Estimate floor area, surface area, or footprint of any trapezoid-shaped object — from a tile to a parcel of land.

3

Unit conversions

Enter dimensions in any common unit and instantly read the area in mm², cm², m², ha, km², in², ft², yd², acres, and mi².

4

Engineering checks

Quickly verify trapezoid area calculations done by hand, in a spreadsheet, or in CAD software.

5

Education & teaching

Use the diagram, step-by-step panel, and area conversion panel as a teaching aid for geometry classes.

6

Reference & quick checks

Look up the trapezoid formula, the result format, and equivalent unit values in a single page.

Best Practices

  • Use consistent units. Every length input must use the same unit. The output area is automatically in the square of that unit.
  • Choose the correct measurement. Read the input labels carefully — many trapezoid formulas distinguish between perpendicular height and slant length.
  • Don't round inputs prematurely. Keep the full precision of your inputs; the calculator only rounds the displayed result.

Why Trapezoid Area Matters

Architecture & construction

Trapezoid shapes appear in floor plans, panel layouts, roof sections, and structural members — accurate area drives material take-offs.

Engineering & design

Cross-sections, plates, and panels are often trapezoid-shaped; their area drives stress, weight, and cost calculations.

Surveying & land use

Surveyors decompose irregular plots into trapezoid-shaped patches; summing the areas gives the total parcel size.

Academia & education

Trapezoid area is a standard topic in primary, secondary, and undergraduate geometry curricula worldwide.

Common Mistakes

  • Mixing length and width units. If one side is in feet and the other in inches, convert first or the area will be off by a factor of 12.
  • Forgetting to square the unit. Area is reported in unit² (m², ft², etc.). The calculator adds the square automatically.
  • Confusing perimeter and area. Perimeter is a linear measurement around the boundary; area is the 2D space inside it.

Core Formula

Formula

A = ½(b₁ + b₂) × h

Area is always returned in your input unit squared. The conversion panel translates the result into mm², cm², m², ha, km², in², ft², yd², acres, and mi² so you can compare across unit systems.

Methodology & Accuracy

Every calculation runs entirely in your browser using JavaScript's full double-precision arithmetic (about 15–17 significant digits internally). The displayed result is rounded to four significant figures by default; numbers outside the 0.0001 to 999,999,999 range switch automatically to scientific notation. The trapezoid formula used here is the standard Euclidean-geometry identity, sourced from the same textbooks used in secondary-school and university geometry courses.

Frequently Asked Questions

Area equals the average of the two parallel bases times the height: A = ½(b₁ + b₂) × h. Height must be measured perpendicular to the parallel bases.

Also called the midsegment, the median is the line segment joining the midpoints of the two non-parallel sides. Its length equals the average of the two bases: m = (b₁ + b₂) / 2.

In American English, a trapezoid is a quadrilateral with exactly one pair of parallel sides. In British English, the same shape is called a trapezium. Both refer to the same figure.

No — the perimeter is the sum of all four sides, so you need both bases and both non-parallel legs. The area only needs the bases and the height.

If b₁ = b₂, the figure is a parallelogram (or a rectangle, if the angles are right angles), and the formula collapses to A = b × h.

Related Calculators

Other geometry and measurement tools that pair with area calculations.