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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 CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance · all published modes
Input interpretation
Enter values to calculate.
Result
—
Verified scope
all published modes
Assurance
Core
Declared partition coverage
PASS · 8/8 declared partitions (rectangle, square, regular-polygon, annulus, parallelogram, trapezoid, irregular-polygon, invalid-domain) · Matrix
Known limitations
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Isosceles trapezoid area, perimeter, legs, and an engine-linked figure of the bases and height.
Scope
Euclidean plane
Verification
Engine tested · Specification checked · v1.5.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance · all published modes· View Manifest · CVP overview · Specification
Versions
Calculation 1.5.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-22.geometry-cvp
Verification revision
2026-09-22.geometry-cvp · 4/4 property · digest dcd9f429cc7c
Legacy regression
25/25 tests · Production surface contract 5/5
Trust layers
Verification VERIFIED · Production CURRENT · Overall CVP state: VERIFIED under CVP 1.0.0-proposed
Reference
O1 model · O2 expected_values · O2 numerical_behavior
Interfaces
PASS · UI (SSR) / REST / MCP — ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only.
Supplemental domain review
Not performed
Named expert review
Not performed
CVP suite
10/10 golden · 5/5 CVP boundary · 11/11 invalid · 4/4 property · 5/5 cross-interface · 5/5 cross-calculator · 5/5 CVP contract · Manifest
Specification basis
  • ISO 80000-2:2019 Quantities and units — Mathematics
Specification basis
Evidence
9 legacy golden · 5 legacy boundary · legacy regression suite · 10/10 oracle-backed golden · 11/11 invalid · Artifact integrity PASS
This calculator CURRENT · Public schema 1.5.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓
Semantic contract
PASS
Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

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. The figure updates with a, b, and h.

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 1.5.0 · 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, legs, and an engine-linked figure of the 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 5/5 · 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
1.5.0

Other calculators in this family: Annulus Calculator, Arc Calculator, Circle Calculator, Conic Section Calculator, Ellipse Calculator, Hyperbola Calculator, Irregular Polygon Calculator, Parabola Calculator . Explore all Geometry.

→ Annulus Calculator Annulus A = π(R² − r²) and P = 2π(R + r) with outer R > inner r. Same engine as Plane Geometry. Not /circle. Not a square. Not CAS. Runs locally. › → Arc Calculator Circle arc s = r θ from radius and central angle. Same engine as Circle. Not /sector. Not /spherical-sector. Not CAS. Runs locally. › → Circle Calculator Compute diameter, circumference, and area from r, or arc and sector from a central angle. Discovery /sector, /arc. Not the Pythagorean page. Not /spherical-sector. 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. › → Ellipse Calculator Standard ellipse x²/a² + y²/b² = 1. Same engine as Conic Section. a = b is a valid ellipse with e = 0; the circle-only page is /circle. Not CAS. Runs locally. › → Hyperbola Calculator Standard hyperbola x²/a² − y²/b² = 1 (horizontal) or y²/a² − x²/b² = 1 (vertical). Same engine as Conic Section. Not CAS. Runs locally. › → Irregular Polygon Calculator Shoelace area of a simple 3–8 vertex polygon. Same engine as Plane Geometry. Not /regular-polygon. Not a triangle solver. Not CAS. Runs locally. › → Parabola Calculator Standard parabola x² = 4py (vertical) or y² = 4px (horizontal). Same engine as Conic Section. p ≠ 0. Not CAS. Runs locally. ›

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.