Area of a Trapezoid Calculator

Calculate the area of a trapezoid using A = ½(b₁+b₂)×h. Find area from parallel base lengths and height, or from all four sides using the general trapezoid formula.

📐 Geometry📐 A = ½(b₁ + b₂) × h🔢 Math
Base 1 (b₁)
Base 2 (b₂)
Height (h)
Please enter valid values.

Formula & Reference

VariableSymbolFormulaUnits
Area of a Trapezoid CalculatorA = ½(b₁ + b₂) × hsquare units

Step-by-Step Examples

Example 1
Standard

b₁=6, b₂=10, h=4.

  • A=½(6+10)×4=½×16×4=32
✓ A = 32 sq units
Example 2
Road Cross-Section

A road cross-section trapezoid: b₁=8m, b₂=12m, h=3m.

  • A=½(8+12)×3=½×20×3=30 m²
✓ A = 30 m²
Example 3
Equal Bases = Rectangle

b₁=b₂=5, h=3.

  • A=½(5+5)×3=15 = 5×3
  • When b₁=b₂, trapezoid becomes rectangle
✓ A = 15 (becomes rectangle)

Real-World Applications

Common Mistakes to Avoid

⚠️
Confusing b₁, b₂ with the legs

b₁ and b₂ are the two parallel sides (bases). The legs are the non-parallel sides. Only the parallel bases go in the formula.

⚠️
Height is perpendicular distance

Height h is the perpendicular distance between the two parallel bases, NOT the length of the slanted legs.

⚠️
Isosceles vs general trapezoid

An isosceles trapezoid has equal legs. The area formula A=½(b₁+b₂)h works for both.

Frequently Asked Questions

What is a trapezoid?
A quadrilateral with exactly one pair of parallel sides (the bases). If both pairs are parallel, it is a parallelogram.
What is the median of a trapezoid?
The segment connecting midpoints of the legs. Its length = (b₁+b₂)/2. Area = median × height.
How does the formula relate to parallelogram?
A trapezoid can be paired with a flipped copy to form a parallelogram with base (b₁+b₂) and height h. So trapezoid area = ½ of parallelogram area.
What is the trapezoidal rule?
Numerical integration method: approximate area under curve by summing trapezoid areas. A≈h/2×(y₀+2y₁+...+2y_{n-1}+yₙ).
How do I find the height from the sides?
For isosceles trapezoid with leg length l: h = √(l²−((b₂−b₁)/2)²) by the Pythagorean theorem.

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Formula Explorer connections

Interpretation: This relationship connects dimensions, coordinates, angles or trigonometric ratios to a geometric measurement. Assumption: Use a consistent angle mode and length unit, identify the intended shape or coordinate system, and verify that the supplied dimensions form valid geometry.

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