Free Area of Trapezoid Calculator – Instant, Accurate & Ad-Free
Calculate the area of a trapezoid using two parallel bases and height
Trapezoid Diagram
Legend:
a = Base 1 (bottom) • b = Base 2 (top) • h = Height
c = Left side • d = Right side
α, β, γ, δ = Interior angles
Trapezoid Area Formula:
Area = (1/2) × (base1 + base2) × height
or
Area = [(a + b) / 2] × h
What is a Trapezoid?
A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called bases (a and b), and the perpendicular distance between them is the height (h).
Examples:
- Base1 = 10, Base2 = 6, Height = 5 → Area = 40 sq units
- Base1 = 8, Base2 = 12, Height = 4 → Area = 40 sq units
- Base1 = 7, Base2 = 5, Height = 6 → Area = 36 sq units
Applications:
- Architecture and construction
- Land area calculations
- Geometry problems
- Engineering designs
Find the area of any trapezoid in seconds with our Free Area of Trapezoid Calculator. Whether you’re working on geometry homework, engineering projects, or construction measurements, this smart tool gives you instant, accurate results — no manual math required.
At Digital Calculator, we make geometry simple and precise. Our Area of Trapezoid Calculator can calculate using bases and height, side lengths, diagonals, or angles. With one click, you’ll get the exact area of any trapezoid — from basic to complex — instantly.
What Is a Trapezoid?
A trapezoid (also called a trapezium in some countries) is a quadrilateral with one pair of parallel sides. The parallel sides are known as bases, and the non-parallel sides are called legs.
In simple terms, a trapezoid looks like a slanted rectangle — wider at one end and narrower at the other.
The area of a trapezoid represents the amount of space enclosed between its four sides, measured in square units (like cm², m², or ft²).
Area of Trapezoid Formula
The most common formula to find the area of a trapezoid is:
Area = ½ × (a + b) × h
Where:
a = length of the first base
b = length of the second base
h = height (the perpendicular distance between the two bases)
This formula works for all trapezoids — whether they are right-angled, isosceles, or scalene.
Example:
If base₁ (a) = 10 cm, base₂ (b) = 6 cm, and height (h) = 5 cm:
Area = ½ × (10 + 6) × 5
Area = ½ × 16 × 5 = 8 × 5 = 40 cm²
Result: The area of the trapezoid is 40 cm².
Alternative Formulas for Area of a Trapezoid
Depending on which dimensions you know, there are several ways to find the area of a trapezoid. Our calculator supports all of them automatically.
1. Using Bases and Height (Standard Formula)
Formula:
A = ½ × (a + b) × h
Example:
a = 12 cm, b = 8 cm, h = 10 cm
A = ½ × (12 + 8) × 10 = 100 cm²
Answer: 100 cm²
2. Using Side Lengths (If Height Unknown)
If you know all four sides — a, b, c, and d — but not the height, use the trapezoid area formula derived from Bretschneider’s formula.
This formula is complex for manual use, so our calculator computes it automatically.
3. Using Diagonals and Angle Between Them
Formula:
A = ½ × d₁ × d₂ × sin(θ)
Example:
d₁ = 8 cm, d₂ = 10 cm, θ = 60°
A = ½ × 8 × 10 × sin(60°) = 34.64 cm²
Answer: 34.64 cm²
4. Using Median (Average of Bases) and Height
Formula:
Median (m) = (a + b) / 2
Area = m × h
Example:
a = 10 cm, b = 14 cm, h = 6 cm
m = (10 + 14) / 2 = 12 cm
Area = 12 × 6 = 72 cm²
Answer: 72 cm²
How to Use the Free Area of Trapezoid Calculator
Our Free Area of Trapezoid Calculator is designed to be intuitive for learners, teachers, engineers, and architects alike.
Select what you know — bases & height, sides, or diagonals.
Enter the values in your preferred unit.
Click “Calculate.”
Instantly get the area, step-by-step breakdown, and conversion to square units.
Quickly reset and calculate another trapezoid without leaving the page.
Try the Free Area of Trapezoid Calculator on Digital Calculator — get instant, accurate, ad-free results.
Step-by-Step Examples
Example 1: Using Bases and Height
Base₁ = 10 m, Base₂ = 6 m, Height = 4 m
Area = ½ × (10 + 6) × 4 = 32 m²
Result: 32 m²
Example 2: Using Median and Height
Median = (a + b) / 2 = (9 + 5) / 2 = 7
Height = 8 cm
Area = 7 × 8 = 56 cm²
Result: 56 cm²
Example 3: Using Diagonals and Angle
d₁ = 6 cm, d₂ = 10 cm, θ = 45°
Area = ½ × 6 × 10 × sin(45°) = 21.21 cm²
Result: 21.21 cm²
Example 4: Unit Conversion
If the area is 1.2 m²,
Convert to cm²: 1 m² = 10,000 cm²
Area = 1.2 × 10,000 = 12,000 cm²
Converted Area: 12,000 cm²
Our calculator automatically converts between standard units like cm², m², ft², and in².
Area of Trapezoid Formula Summary Table
| Known Parameters | Formula | Example | Result |
|---|---|---|---|
| Bases & Height | ½ × (a + b) × h | a=10, b=6, h=5 | 40 |
| Median & Height | m × h | m=7, h=8 | 56 |
| Diagonals & Angle | ½ × d₁ × d₂ × sin(θ) | d₁=8, d₂=10, θ=60° | 34.64 |
| All Sides Known | Bretschneider’s Formula | a=10, b=8, c=7, d=5 | 59.4 |
| Isosceles Trapezoid | h = √[l² – ((a – b)² / 4)], then A=½×(a+b)×h | l=5, a=10, b=6 | 40 |
Our calculator automatically chooses the correct formula based on your inputs — giving you error-free results every time.
Understanding Trapezoid Geometry
To calculate accurately, it helps to know a few trapezoid properties:
Bases (a and b): The two parallel sides.
Legs (c and d): The non-parallel sides.
Height (h): The perpendicular distance between the bases.
Median (m): The average length of the bases.
Diagonals (d₁, d₂): Lines connecting opposite corners.
These components define whether the trapezoid is right, isosceles, or scalene — and which formula to use.
Types of Trapezoids
| Type | Description | Formula Example |
|---|---|---|
| Right Trapezoid | One angle is 90° | Area = ½ × (a + b) × h |
| Isosceles Trapezoid | Non-parallel sides equal | Area = ½ × (a + b) × √[l² – ((a – b)² / 4)] |
| Scalene Trapezoid | All sides different | Use Bretschneider’s formula |
| Symmetrical Trapezoid | Has an axis of symmetry | Area = ½ × (a + b) × h |
Our calculator supports all trapezoid types — giving correct results regardless of complexity.
Real-Life Applications of Trapezoid Area
The trapezoid area formula is widely used in:
Architecture & Construction – For floor space, sloped roofs, ramps, and bridges.
Engineering – To calculate trapezoidal sections for beams and channels.
Education – Helps students learn geometric reasoning.
Graphic Design & 3D Modeling – Used in shape and proportion calculations.
Land Measurement – For irregular plots shaped like trapezoids.
No matter your application, our Free Area of Trapezoid Calculator saves time and ensures precision.
Common Mistakes to Avoid
Using slanted sides instead of height — always use the perpendicular height.
Mixing up bases — both bases must be parallel sides.
Ignoring units — ensure all measurements use the same unit.
Incorrect sine angle usage — keep units consistent (degrees/radians).
Rounding too early — use 3–4 decimal places for precision.
Our calculator corrects unit mismatches and ensures the right formula every time.
Benefits of Using Digital Calculator’s Area of Trapezoid Tool
100% Free and Ad-Free
Multiple Calculation Methods
Instant Accuracy
Educational Step-by-Step Display
Supports All Units (cm, m, ft, in)
Optimized for Mobile and Desktop
Use the Free Area of Trapezoid Calculator on Digital Calculator — accurate, fast, and educational.
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