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Math calculator

Trapezoid Calculator

Isosceles trapezoid A = (a+b)h/2 from two bases and height. Same engine as Plane Geometry. Not /trapezoidal-rule. Not the fluid trapezoid. Not CAS. Runs locally.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary Engine tested · Specification checked · 25/25 tests · Production surface contract 3/3 · v1.3.0
Input interpretation
Enter values to calculate.
Result
—
Model
Isosceles trapezoid area, perimeter, and legs from two bases and height.
Scope
Euclidean plane
Verification
Engine tested · 25/25 tests · Production surface contract 3/3 · Specification checked · v1.3.0
Named expert review
Optional · Not performed
Specification basis
  • ISO 80000-2:2019 Quantities and units — Mathematics
Specification basis
Evidence
9 golden · 5 boundary · 11 property · Production surface contract 3/3 · Artifact integrity PASS
Production
Embedded snapshot: unpublished · Build schema 1.3.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (2 capabilities; 162 remain CURRENT) @ 2026-09-20T09:01:12.147Z
Semantic contract
PASS

Formulas

Core equations used by this calculator.

AreaA = (a+b)h/2
Isosceles legsc = √(((a − b)/2)² + h²)
iSame engine as /plane-geometry. The integral trapezoid is /trapezoidal-rule. Open-channel trapezoid stays on /calc/physics.

How to use

1

Enter bases a, b and height h

All must be positive. Default a=2, b=4, h=3. Equal bases a=b are a valid rectangle.

2

Read A, P, and the legs

2-4-3 has area 9. Equal bases 3 and 3 with h=4 match the 3×4 rectangle.

Example calculations

Common configurations with formula and result.

ϟ

2-4-3

a = 2, b = 4, h = 3

A = (2+4)×3/2
A=9
ϟ

Rectangle identity

a = 3, b = 3, h = 4

A = 12, P = 14
A=12, P=14

Trapezoid calculator specification

Version 1.3.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
An isosceles trapezoid of parallel bases a>0, b>0 and height h>0 has area (a+b)h/2 and legs √(((a−b)/2)²+h²). a=b recovers a rectangle. This page is mode=trapezoid on math.geometry.plane. Not /trapezoidal-rule. Not the fluid trapezoid. Not CAS.
What it calculates
Isosceles trapezoid area, perimeter, and legs from two bases and height.
Inputs
  • a
  • b
  • h
Outputs
  • area
  • perimeter
  • leg
  • midsegment
  • height
Formula
A = (a+b)h/2, P = a+b+2√(((a−b)/2)²+h²)
Assumptions
  • Euclidean plane
  • Isosceles legs from the overhang
  • a=b is a valid rectangle
  • Not /trapezoidal-rule
  • Not the fluid trapezoid
  • Not CAS
Units
  • length (consistent units)
  • area (length²)
Boundary conditions
  • a ≤ 0 or b ≤ 0 or h ≤ 0 → VALUE_MUST_BE_POSITIVE
  • unknown mode → INVALID_MODE
Example
a=2 b=4 h=3 → A=9
Validation cases

3 published on this page · 25/25 tests · Production surface contract 3/3 · View evidence

  • a=2 b=4 h=3 → A=9
  • a=3 b=3 h=4 → A=12 P=14
  • a=2 b=4 h=0 → VALUE_MUST_BE_POSITIVE
Specification basis
  • ISO 80000-2:2019 Quantities and units — Mathematics
Calculation version
1.3.0

Other calculators in this family: Angle Between Lines Calculator, Circle Calculator, Cone Calculator, Conic Section Calculator, Coordinate Geometry Calculator, Cross Product Calculator, Cylinder Calculator, Dot Product Calculator . Explore all Geometry.

→ Angle Between Lines Calculator Acute angle between two plane lines, each given by two points. Parallel is 0°. Perpendicular is 90°. Degenerate points are invalid. Same engine as Coordinate Geometry. Not a second engine. Not CAS. Runs locally. › → Circle Calculator Compute diameter, circumference, and area from r, or arc and sector from a central angle. Not the Pythagorean page. Runs locally. › → Cone Calculator Right circular cone V = (1/3)πr²h and slant l = √(r²+h²). Same engine as Solid Geometry. Not ISO 5167-5. Not CAS. Runs locally. › → Conic Section Calculator Axis-aligned ellipse, parabola, and hyperbola in standard form. Discovery /ellipse, /parabola, /hyperbola. Not the circle-only page. Not coordinate geometry. Not CAS. Runs locally. › → Coordinate Geometry Calculator Distance, midpoint, and slope of two points in the plane. Line through two points is /line-equation. Point-to-line distance is /point-line-distance. Intersection is /line-intersection. Angle is /angle-between-lines. Not the Pythagorean-only page. Runs locally. › → Cross Product Calculator Vector product u × v in R³. 2-D uses uz = vz = 0. Same engine as Vector. Not a matrix. Not CAS. Runs locally. › → Cylinder Calculator Right circular cylinder V = πr²h and A = 2πr(r+h). Same engine as Solid Geometry. Not CAS. Runs locally. › → Dot Product Calculator Scalar product u · v = ux vx + uy vy + uz vz. Same engine as Vector. Not a matrix. Not CAS. Runs locally. ›
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Frequently asked questions

Key distinctions behind the calculation.

Is this a second plane engine?

No. It is mode=trapezoid on math.geometry.plane, the same engine as /calc/math/plane-geometry.

Is this the integral trapezoidal rule?

No. Numerical integration stays on /calc/math/trapezoidal-rule. This page is a Euclidean plane figure.

Is this the fluid trapezoid?

No. Open-channel trapezoid depth stays on /calc/physics. This seed is an isosceles plane trapezoid.

Where does this run?

Locally in the browser by default. REST and MCP call the same plane-geometry engine.