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Geometry

Trapezoid Area Calculator

A = ½(b₁+b₂)h. Free online Trapezoid Area Calculator. Calculate trapezoid area online — fast, accurate, mobile-friendly, no signup needed.

Area = ½ · (a + b) · h.
Area
40

Derivation

  1. ├── 01Givenb1 = 6, b2 = 10, h = 5
  2. ├── 02Formula.5 × (e.b1+e.b2) × e.h
  3. ├── 03Substitute.5 × (e.6+e.10) × e.5
  4. └── 04Compute Area40
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§01What is

Understanding the Trapezoid Area Calculator

The Trapezoid Area Calculator computes Area from 3 inputs: base₁, base₂, height. A = ½(b₁+b₂)h.

Geometry is what turns raw measurements into useful answers about space — how much paint, how big a yard, how much material a project will need. Every craftsperson, architect, and DIYer reaches for these formulas regularly. The Trapezoid Area Calculator sits in that toolkit — it A = ½(b₁+b₂)h. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

.5 × (e.b1+e.b2) × e.h

Where

b1
Base₁
b2
Base₂
h
Height
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Base₁ = 6, Base₂ = 10, Height = 5.

  1. 01Start by noting the input — Base₁: 6.
  2. 02Start by noting the input — Base₂: 10.
  3. 03Start by noting the input — Height: 5.
  4. 04Substitute these values into the formula: .5 × (e.b1+e.b2) × e.h
  5. 05Compute Area: the calculator returns 40.
  6. 06Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Trapezoid Area Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

Base₁ halved

b1 = 3 (from 6)

Keep every other input at its default and halve the base₁. See how area responds.

  1. 01New Base₁: 3
  2. 02Baseline Area: 40
  3. 03New Area: 32.5
  4. 04Area decreases by 18.8% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Base₁ doubled

b1 = 12 (from 6)

Keep every other input at its default and double the base₁. See how area responds.

  1. 01New Base₁: 12
  2. 02Baseline Area: 40
  3. 03New Area: 55
  4. 04Area increases by 37.5% → use this sensitivity to plan for real-world variation.
03 · PATTERN

Base₂ halved

b2 = 5 (from 10)

Keep every other input at its default and halve the base₂. See how area responds.

  1. 01New Base₂: 5
  2. 02Baseline Area: 40
  3. 03New Area: 27.5
  4. 04Area decreases by 31.3% → use this sensitivity to plan for real-world variation.
04 · PATTERN

Base₂ doubled

b2 = 20 (from 10)

Keep every other input at its default and double the base₂. See how area responds.

  1. 01New Base₂: 20
  2. 02Baseline Area: 40
  3. 03New Area: 65
  4. 04Area increases by 62.5% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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