Area of a Trapezoid Calculator

Free online Area of a Trapezoid calculator — convert units, see steps, download results and view a live pie chart. No signup, no API, 100% client-side.

Select base 1 unit
Select base 2 unit
Select height unit
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Result accuracy

📐 Trapezoid Diagram

📊 Trapezoid Visualization

ℹ️ What is the Area of a Trapezoid?

Area = (Base₁ + Base₂) / 2 × Height

The area of a trapezoid is the amount of space enclosed within its four sides. A trapezoid (or trapezium) is a quadrilateral with at least one pair of parallel sides. The parallel sides are called bases, and the perpendicular distance between them is the height. The area is calculated by taking the average of the two bases and multiplying by the height.

📚 Step-by-Step Examples

Example 1: Trapezoid with bases 8m and 5m, height 4m
Step 1: Identify the bases and height: Base₁ = 8m, Base₂ = 5m, Height = 4m
Step 2: Apply the formula: Area = (Base₁ + Base₂) / 2 × Height
Step 3: Calculate: (8 + 5) / 2 = 6.5, then 6.5 × 4 = 26
Result: The area is 26 square meters.
Example 2: Trapezoid with bases 12cm and 7cm, height 5cm
Step 1: Identify the bases and height: Base₁ = 12cm, Base₂ = 7cm, Height = 5cm
Step 2: Apply the formula: Area = (Base₁ + Base₂) / 2 × Height
Step 3: Calculate: (12 + 7) / 2 = 9.5, then 9.5 × 5 = 47.5
Result: The area is 47.5 square centimeters.
Example 3: Trapezoid with bases 10.5in and 6.2in, height 4in
Step 1: Identify the bases and height: Base₁ = 10.5in, Base₂ = 6.2in, Height = 4in
Step 2: Apply the formula: Area = (Base₁ + Base₂) / 2 × Height
Step 3: Calculate: (10.5 + 6.2) / 2 = 8.35, then 8.35 × 4 = 33.4
Result: The area is 33.4 square inches.

❓ Frequently Asked Questions

What is the formula for the area of a trapezoid?
The area of a trapezoid is calculated using the formula: Area = (Base₁ + Base₂) / 2 × Height. This formula works for any trapezoid where you know the lengths of both bases and the height.
What is a trapezoid?
A trapezoid (or trapezium) is a quadrilateral with at least one pair of parallel sides. The parallel sides are called bases, and the non-parallel sides are called legs. The height is the perpendicular distance between the bases.
Can I calculate the area if I only know the sides?
If you know all four sides but not the height, you need to calculate the height first using the Pythagorean theorem or other geometric methods. This calculator requires the height for direct calculation.
What units are used for area measurement?
Area is measured in square units. Common units include square meters (m²), square centimeters (cm²), square inches (in²), and square feet (ft²). The calculator automatically converts between these units.
What’s the difference between a trapezoid and a parallelogram?
A parallelogram has two pairs of parallel sides, while a trapezoid has only one pair of parallel sides. All parallelograms are trapezoids, but not all trapezoids are parallelograms.
Can the bases be of any length?
Yes, the bases can be any positive length. However, for a valid trapezoid, the sum of the lengths of any three sides must be greater than the length of the remaining side.

📐 Real-World Applications

Where is trapezoid area calculation used in daily life?
Trapezoid area calculations are essential in many real-world scenarios:
  • Architecture: Calculating floor areas in rooms with trapezoidal shapes
  • Engineering: Determining cross-sectional areas of beams and channels
  • Land Surveying: Calculating areas of irregular land plots
  • Construction: Estimating materials for trapezoidal roofs or windows
  • Manufacturing: Calculating material requirements for trapezoidal components
How accurate is this calculator?
This calculator provides highly accurate results based on mathematical formulas. You can control the precision using the decimal places selector. The calculations account for unit conversions and maintain mathematical accuracy throughout the process.