Trapezoid Area Formula Calculator

This calculator works out the area of a trapezoid (also called a trapezium in some countries) from the lengths of its two parallel sides and its height. You enter the base lengths and the height, and you get the area in square units instantly, along with a step-by-step breakdown of the formula.

Formula

The area of a trapezoid is given by the formula:

Area = (a + b) × h / 2

• a = length of one parallel side (base 1), in meters (m)
• b = length of the other parallel side (base 2), in meters (m)
• h = perpendicular distance between the two bases (height), in meters (m)

The result is in square meters (m²) if all inputs are in meters. The formula works for any unit as long as all three values use the same unit.

Worked Example

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

1. Add the bases: 8 + 5 = 13 m
2. Multiply by the height: 13 × 4 = 52 m²
3. Divide by 2: 52 / 2 = 26 m²

The calculator shows 26.00 m², matching the formula exactly.

Why the Formula Works

A trapezoid can be thought of as half of a parallelogram. If you duplicate a trapezoid, rotate it 180°, and join it along one of the non-parallel sides, you get a parallelogram whose base is (a + b) and whose height is h. The area of that parallelogram is (a + b) × h. Since the trapezoid is exactly half of that, its area is (a + b) × h / 2. This geometric derivation is the standard explanation found in most geometry textbooks.

When to Use This Calculator

This calculator is useful in construction, landscaping, fabric cutting, and any project where you need to find the area of a four-sided shape with one pair of parallel sides. For example:

• Calculating the floor area of a trapezoidal room
• Estimating the amount of soil or mulch for a trapezoidal garden bed
• Finding the surface area of a trapezoidal prism face
• Determining the size of a custom-shaped piece of glass or wood

If you need the area in square feet, yards, or centimeters, simply enter the base lengths and height in those units—the calculator will output the area in the corresponding square unit.

Common Mistakes and How to Avoid Them

• Using the slanted side instead of the height: The height must be measured perpendicular (at a right angle) to the bases, not along the slanted edge. This is the most frequent error.
• Mixing units: If one base is in meters and the other in centimeters, the result is wrong. Convert all inputs to the same unit first.
• Forgetting to divide by 2: The formula includes a factor of 1/2. Some people multiply the sum of the bases by the height but forget the division.
• Confusing a trapezoid with a parallelogram: A parallelogram has two pairs of parallel sides; a trapezoid has only one. The formula is different for a parallelogram (Area = base × height).

Limitations of the Formula

The formula assumes a standard trapezoid with straight sides and a constant height. It does not apply to:

• Shapes with curved sides (like a circular segment)
• Three-dimensional volumes (use the prism volume formula instead)
• Irregular quadrilaterals with no parallel sides (use triangulation or a general polygon area method)

Also note that the formula is independent of the lengths of the non-parallel sides. Two trapezoids with the same bases and height but different slanted side lengths will have the same area.

Frequently Asked Questions

What if the trapezoid is upside down or rotated?

Orientation does not matter. The formula uses only the lengths of the parallel sides and the perpendicular height, regardless of which side is on top or how the shape is rotated.

Can I use this for a trapezium (UK terminology)?

Yes. In British English, a trapezium is the same shape as a trapezoid in American English (one pair of parallel sides). The formula is identical. Be aware that in some countries the terms are reversed, but the shape and calculation remain the same.

How do I find the height if I only know the side lengths?

If you know the lengths of all four sides, you can find the height by drawing a perpendicular from one base to the other and using the Pythagorean theorem on the resulting right triangles. However, that requires additional steps and is not built into this calculator.

Is the area the same as the surface area of a trapezoidal prism?

No. The area calculated here is the two-dimensional area of a single trapezoidal face. A trapezoidal prism has two such faces plus four rectangular faces, so its total surface area is larger. This calculator only gives the area of the trapezoid itself.

What if my bases are in feet and my height is in inches?

Convert everything to the same unit first. For example, convert feet to inches (multiply by 12) or inches to feet (divide by 12), then enter the values. The calculator will output the area in the corresponding square unit.

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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) * h / 2 | 2