Trapezoid Area: Formula, Example, and Calculator

Calculate the area of a trapezoid by adding the lengths of its two parallel sides, multiplying that sum by the perpendicular height, and dividing by 2. Enter the two bases and height in the calculator to get the area in square units.

Formula

The area formula is A = (a + b)h / 2, or equivalently A = h(a + b) ÷ 2. Here, A is the area in square units, a and b are the lengths of the two parallel sides (the bases), and h is the perpendicular distance between those sides, in the same linear unit as the bases.

The calculator’s second result, average base length, is (a + b) / 2. Multiplying that average by the height gives the same area: A = average base × h. For example, if the measurements are in inches, the area is in square inches; if they are in centimeters, it is in square centimeters. The formula itself does not depend on the chosen unit system.

Worked Example

Using the calculator’s default values, the first base is 8 units, the second base is 14 units, and the height is 5 units.

1. Add the bases: 8 + 14 = 22 units.
2. Multiply by the height: 22 × 5 = 110 square units.
3. Divide by 2: 110 ÷ 2 = 55 square units.

The average base is (8 + 14) ÷ 2 = 11 units, and 11 × 5 also equals 55 square units. Both methods produce the same area.

What the Formula Measures

A trapezoid is a four-sided shape with a pair of parallel sides. Those parallel sides are called bases, even if one is shorter than the other or the shape is turned sideways. The height is the shortest distance from one base to the other: specifically, the perpendicular distance, which meets the bases at a right angle.

The formula can be understood by comparing the trapezoid with a rectangle. Its average base length is halfway between the two base lengths. A rectangle with that average length and the same height has exactly the trapezoid’s area. Another way to see the idea is to place two identical trapezoids together to form a parallelogram whose base is a + b and whose height is h. One trapezoid is half that parallelogram, giving (a + b)h / 2.

How to Measure and Use the Result

Identify the parallel sides first, then measure their lengths and the perpendicular separation between them. For a drawing, the height might be marked with a right-angle symbol. In a physical measurement, use a square, a reliable diagram, or another method that establishes the right angle rather than estimating a slanted edge.

• Use consistent units: Do not enter one base in feet and the other in inches without converting. Convert all three measurements to the same unit before calculating.
• Report square units: A result based on meters is in square meters (m²), not meters. A result based on feet is in square feet (ft²).
• Interpret the number as flat coverage: Area describes a two-dimensional surface. It is not perimeter, which measures boundary length, or volume, which measures three-dimensional space.
• Keep useful precision: Retain extra digits during intermediate steps, then round the final area to match the accuracy of the measurements.

For a practical example, a trapezoidal garden bed with bases of 3 ft and 5 ft and a perpendicular height of 4 ft has area (3 + 5) × 4 ÷ 2 = 16 ft². If the same dimensions are measured in meters instead, the answer is in m². Square-unit conversions must be squared: 1 m² equals 10.7639 ft², approximately, not 3.28084 ft².

Common Mistakes and Limits

The most frequent error is using a sloping side as the height. A slanted leg is usually longer than the perpendicular separation, so substituting it can overstate the area. The height does not have to fall inside the trapezoid: for some slanted shapes, the perpendicular distance between the parallel lines extends outside the four-sided outline.

Another common error is adding the bases but forgetting to divide by 2. The formula uses their average, not their total. It is also important to use the two parallel sides—not the nonparallel legs—in the sum. If the bases are equal, the trapezoid is a parallelogram and the formula reduces to base × height, which is a useful check.

This formula assumes a flat, straight-edged trapezoid and accurate measurements. It does not calculate the area of a curved shape or account for an uneven real-world surface. For a drawing, a scale error or imprecise measurements can affect the result even when the arithmetic is correct. A calculator result should not imply more precision than the supplied dimensions support.

Frequently Asked Questions

What is the formula for the area of a trapezoid?
Use A = (a + b)h / 2, where a and b are the parallel base lengths and h is the perpendicular height.

How do I find the height of a trapezoid?
Measure the perpendicular distance between the parallel bases. A sloping side is not the height unless it meets the bases at a right angle.

Can I calculate the area if I know only the four side lengths?
Not in general. Side lengths alone may not determine the height or the shape uniquely. You need enough additional information to establish the perpendicular height, such as an angle or a diagonal with suitable measurements.

Does the trapezoid formula work when the shape is tilted?
Yes. Rotating the shape does not change its area. Use the lengths of the parallel sides and their perpendicular separation, regardless of which way the trapezoid is oriented.

What units should I use for trapezoid area?
Use one consistent linear unit for the bases and height. The answer is in the corresponding square unit, such as cm², m², in², or ft².

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in a | First base | units | 8 | 0
in b | Second base | units | 14 | 0
in h | Height | units | 5 | 0
out area | Trapezoid area | square units | (a + b) * h / 2 | 2
out mid | Average base length | units | (a + b) / 2 | 2