Area of a Trapezoid: Formula & Examples

The area of a trapezoid is the total space enclosed by its four sides, calculated as the average of the two base lengths multiplied by the height. You enter the lengths of the two parallel sides and the perpendicular height into the calculator below, and it returns the area in square units.

Formula

The standard formula for the area of a trapezoid is:

Area = (a + b) / 2 × h

Where:

• a = length of the first parallel side (base), in meters (or any consistent unit)
• b = length of the second parallel side (base), in the same unit
• h = perpendicular height between the two bases, in the same unit

The result is in square units (e.g., m², cm², ft²). The height must be measured at a right angle to the bases, not along the slanted side.

Worked Example

Using the default values from the calculator: base a = 8 m, base b = 5 m, height h = 4 m.

1. Add the bases: 8 + 5 = 13 m
2. Divide by 2: 13 / 2 = 6.5 m (this is the average base length)
3. Multiply by the height: 6.5 × 4 = 26 m²

The area is 26 square meters, which matches the calculator output.

When to Use the Trapezoid Area Formula

Use this formula whenever you need the area of a four-sided figure with exactly one pair of parallel sides. Common real-world situations include:

• Finding the area of a trapezoidal garden bed or lawn
• Calculating the surface area of a trapezoidal window or roof section
• Determining the cross-sectional area of a canal, ditch, or embankment
• Estimating material quantities for a trapezoidal slab or countertop

If both pairs of opposite sides are parallel, the shape is a parallelogram, and you can use the simpler formula base × height. If no sides are parallel, the trapezoid formula does not apply.

How to Measure the Bases and Height

To get an accurate area, you need the correct measurements:

• Bases (a and b): These are the two parallel sides. Measure them along the straight edge, in the same unit.
• Height (h): This is the shortest distance between the two parallel sides, measured along a line perpendicular to them. Do not measure the slanted leg.

If you only know the lengths of the non-parallel sides and the angles, you can calculate the height using trigonometry (height = side × sin(angle)). But for most practical purposes, a direct perpendicular measurement is easiest.

Common Mistakes and Misconceptions

• Using the slanted side as the height: The height must be perpendicular to the bases. Using the leg length gives a larger, incorrect area.
• Forgetting to average the bases: Some people multiply (a + b) × h without dividing by 2. That gives the area of a parallelogram with base (a+b), which is double the trapezoid area.
• Mixing units: If base a is in meters and base b is in centimeters, convert one to the other first. The area unit will be the square of the unit you used.
• Assuming the height is the same as the side length: This is only true for a rectangle (a special trapezoid). For a slanted trapezoid, the height is always shorter than the leg.

Why the Formula Works

The formula comes from the fact that a trapezoid can be transformed into a rectangle with the same area. If you duplicate the trapezoid, rotate it 180°, and attach it to the original, you get a parallelogram with base (a + b) and height h. That parallelogram has area (a + b) × h. Since the trapezoid is half of that parallelogram, its area is (a + b) × h / 2. This is why the formula is the average of the bases times the height.

Frequently Asked Questions

What if the trapezoid has no right angles?

The formula still works as long as you measure the perpendicular height. The angles do not affect the area calculation; only the base lengths and the height matter.

Can I use the formula for a parallelogram?

Yes, because a parallelogram has two pairs of parallel sides, so it is a special trapezoid. If a = b, the formula becomes (a + a)/2 × h = a × h, which is the standard parallelogram area formula.

What is the difference between a trapezoid and a trapezium?

In American English, a trapezoid has at least one pair of parallel sides, while a trapezium has no parallel sides. In British English, the terms are reversed. This calculator uses the American definition.

How do I find the area if I only know the four side lengths?

You cannot determine the area from side lengths alone because the shape can flex. You also need the height or an angle. If you have the height, use the formula. If you have an angle, you can compute the height using trigonometry.

Does the order of the bases matter?

No, addition is commutative, so swapping a and b gives the same result. Just make sure both are the parallel sides.

What units will the area be in?

The area is in square units of whatever unit you used for the bases and height. For example, if you input meters, the area is in square meters (m²). If you input feet, the area is in square feet (ft²).

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in a | Base a | m | 8 | 0
in b | Base b | m | 5 | 0
in h | Height | m | 4 | 0
out area | Area | m² | (a + b) / 2 * h | 2