Area of a Trapezoid Calculator

What is a Trapezoid?

A trapezoid (known as a trapezium in the UK, Australia, and New Zealand) is a four-sided flat shape (quadrilateral) with at least one pair of parallel sides. These parallel sides are called the bases of the trapezoid, commonly referred to as base $a$ and base $b$. The non-parallel sides are known as the legs. The perpendicular distance between the two parallel bases is called the height ($h$).

Area of a Trapezoid Formula

The area of a trapezoid is calculated by taking the average of the two bases and multiplying it by the height. The mathematical formula for finding the area is:

$$A = \frac{a + b}{2} \times h$$

Where:

$A$ is the area of the trapezoid.
$a$ is the length of the first base (parallel side).
$b$ is the length of the second base (parallel side).
$h$ is the height (perpendicular distance between bases $a$ and $b$).

How to Calculate the Area of a Trapezoid

To find the area of any trapezoid, follow these simple steps:

Measure or identify the lengths of the two parallel bases ($a$ and $b$). Ensure they are in the same unit of measurement.
Measure the perpendicular height ($h$), which is the shortest distance between the parallel bases.
Add the lengths of the two bases together: $(a + b)$.
Divide the sum of the bases by 2 to get their average: $\frac{a + b}{2}$.
Multiply this average by the height: $(\text{average}) \times h$. The resulting value is the total area in square units.

Example Calculation

Suppose you have a trapezoid with base $a = 6\text{ cm}$, base $b = 10\text{ cm}$, and height $h = 5\text{ cm}$.

First, add the bases: $6 + 10 = 16\text{ cm}$.
Second, divide by 2: $16 / 2 = 8\text{ cm}$.
Third, multiply by the height: $8 \times 5 = 40\text{ cm}^2$.
The area of the trapezoid is $40\text{ square centimeters}$.

Related Geometric Tools

If you are working with other geometric shapes, you might find our other calculators helpful:

Use the Area of a Circle Calculator to calculate circle areas from radius or diameter.
Use our general Area Calculator for quick access to multi-shape formulas.

Frequently Asked Questions

What is the difference between a trapezoid and a trapezium?

In American English, a trapezoid is a quadrilateral with one pair of parallel sides, while a trapezium is a quadrilateral with no parallel sides. In British English, the definitions are reversed: a trapezium has one pair of parallel sides, and a trapezoid has no parallel sides. Our calculator works for any quadrilateral with one pair of parallel sides regardless of which term you use.

What unit of measurement should I use for bases and height?

You can use any unit of measurement (such as inches, feet, yards, centimeters, meters, or kilometers) as long as you use the same unit for all three inputs (base a, base b, and height). The output area will be in corresponding square units (e.g. square centimeters or square inches).

Can the area of a trapezoid be negative or zero?

No. In physical geometry, lengths must be positive numbers. Therefore, both bases and the height must be greater than zero, resulting in an area that is also strictly positive.

How does a right trapezoid differ from other trapezoids?

A right trapezoid (or right-angled trapezoid) has two adjacent right angles. For a right trapezoid, one of the non-parallel legs is perpendicular to the bases, meaning that leg's length is equal to the height of the trapezoid. The area formula remains exactly the same.

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