What is the formula for the area of a trapezoid?

The area of a trapezoid is calculated using A = (a + b) / 2 x h, where a and b are the lengths of the two parallel sides (called the bases) and h is the perpendicular height between those bases. This is equivalent to multiplying the average of the two bases by the height. For example, a trapezoid with bases of 6 cm and 10 cm and a height of 4 cm has an area of (6 + 10) / 2 x 4 = 8 x 4 = 32 cm squared.

What is the difference between a trapezoid and a trapezium?

The terms are regional variations of the same shape. In New Zealand, Australia, and the United Kingdom, the shape with one pair of parallel sides is called a trapezium. In the United States and Canada, the same shape is called a trapezoid. On this calculator, the word trapezoid is used in its American sense: a quadrilateral with exactly one pair of parallel sides (called the bases). The area formula A = (a + b) / 2 x h applies regardless of which term you use.

Does it matter which side I enter as base a and which as base b?

No. Because the formula adds the two bases together before dividing by two, the result is identical whether you enter the longer base as a or b. What does matter is that you enter the perpendicular height, which is the vertical distance between the two parallel sides, not the length of either slanting leg. If you have the leg length instead of the height, you can use the Pythagorean theorem to find the perpendicular height first.

Area of a Trapezoid Calculator

Enter the lengths of the two parallel sides (bases) and the perpendicular height to calculate the area of a trapezoid. Uses the standard formula A = (a + b) / 2 x h, where a and b are the bases and h is the height.

The result updates instantly and includes step-by-step working so you can follow every calculation.

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Standard formula A = (a + b) / 2 x h - applicable to all trapezoids and trapeziums.

1. Parallel Sides (Bases)

Base a (first parallel side)

units

Please enter a positive number.

Base b (second parallel side)

units

Please enter a positive number.

Perpendicular height h

units

Please enter a positive number.

2. Unit of Measurement

Length unit

All three values must be in the same unit. The area result is returned in square units of the length you choose (e.g. m gives m²).

Trapezoid Area

Average of Bases

8.00

m (midline length)

Area
32.00
m²

Sum of Bases (a + b)

Not a perimeter - legs excluded

Step-by-step working

A = (a + b) / 2 x h

A = (6 + 10) / 2 x 4

A = 16 / 2 x 4

A = 8 x 4

A = 32 m²

Dimensions

Base a6 m

Base b10 m

Perpendicular height h4 m

Sum of bases (a + b)16 m

Average of bases (a + b) / 28 m

Area32 m²

Notes on Measurement

Height type requiredPerpendicular (not slant)

Shape typeTrapezoid / trapezium

Parallel sidesa and b

FormulaA = (a + b) / 2 x h

Also written asA = ((a + b) x h) / 2

Special caseGeneral trapezoid

How to Calculate the Area of a Trapezoid

A trapezoid (called a trapezium in New Zealand, Australia, and the UK) is a four-sided flat shape with exactly one pair of parallel sides. Those parallel sides are called the bases. The perpendicular distance between the two bases is the height.

The area formula is:

A = (a + b) / 2 x h

where a is the length of the first base, b is the length of the second base, and h is the perpendicular height. You can also write this as A = ((a + b) x h) / 2, which means the same thing: find the average of the two bases, then multiply by the height.

Why the Formula Works

One way to see why this formula is correct is to imagine cutting a trapezoid in half horizontally at the midpoint of its height. You get two smaller trapezoids. If you flip one piece upside down and place it next to the other, the two pieces form a parallelogram whose base equals (a + b) and whose height equals h / 2. The area of a parallelogram is base x height, so the area of the two halves combined is (a + b) x (h / 2), which equals (a + b) / 2 x h. That is the same as the trapezoid area formula.

Another way to think about it: the average of the two bases is the length of the midsegment (the line joining the midpoints of the two non-parallel sides). Multiplying the midsegment by the full height gives the area.

Worked Example

A trapezoidal garden bed has a front edge of 6 m, a back edge of 10 m, and a depth (perpendicular distance between front and back) of 4 m. What is the area?

A = (6 + 10) / 2 x 4 = 16 / 2 x 4 = 8 x 4 = 32 m²

This matches the default output of the calculator above.

Common Mistakes

Using the slant leg instead of the perpendicular height. The formula requires the vertical distance between the two parallel sides, not the length of either angled leg. If you only know the leg length, use the Pythagorean theorem to find h first.
Mixing units. All three inputs (a, b, and h) must be in the same unit. If one side is in centimetres and another in metres, convert before calculating.
Confusing which sides are parallel. Only a and b (the two bases) are parallel. The other two sides (the legs) can be any length or angle.

Special Cases

Shape	Condition	Area formula
General trapezoid	a not equal to b	A = (a + b) / 2 x h
Parallelogram	a = b (both bases equal)	A = a x h (simplifies from formula)
Rectangle	a = b and both legs perpendicular	A = a x h
Right trapezoid	One leg is perpendicular to both bases	A = (a + b) / 2 x h (same formula)
Isosceles trapezoid	Both legs are equal length	A = (a + b) / 2 x h (same formula)

When a equals b, the shape becomes a parallelogram and the formula simplifies to A = a x h. You can verify this by substituting a = b into (a + b) / 2, which gives (a + a) / 2 = a.

Related Calculators

Maths and Stats Calculators: full index of geometry and maths tools.
Area of a Triangle Calculator: A = 1/2 x base x height.
Area of a Rectangle Calculator: A = length x width.
Area of a Circle Calculator: A = pi x r².
Area of a Right Triangle Calculator: A = 1/2 x base x height for right triangles.

Sources and method: Formula A = (a + b) / 2 x h is the standard Euclidean geometry result for the area of a trapezoid, derived from the parallelogram area formula. See: Weisstein, Eric W. "Trapezoid." MathWorld (mathworld.wolfram.com/Trapezoid.html). New Zealand Mathematics Curriculum (nzmaths.co.nz), Level 4 Geometry strand.

This calculator computes area from the inputs you provide. Ensure that the height entered is the perpendicular distance between the two parallel sides, not the length of a slant leg. All inputs must share the same unit of measurement.