# How to Identify a Trapezoid

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You're probably already familiar with squares and rectangles – four-sided quadrilaterals with four right angles. If you were to choose one side of those familiar shapes and either shorten or lengthen that side, you'd get another type of quadrilateral called a trapezoid.

#### TL;DR (Too Long; Didn't Read)

A trapezoid is a quadrilateral (four-sided figure) with only two parallel sides.

## Defining a Trapezoid Shape

The definition of a trapezoid is: a quadrilateral with only two parallel sides. That's almost deceptively simple, so it might be helpful to also understand what a trapezoid is not. If the shape you're looking at doesn't have at least one set of parallel sides, it's not a trapezoid; it's something called a trapezium instead. Similarly, if the shape has two sets of parallel sides, it's not a trapezoid. It's either a rectangle, a parallelogram shape or a rhombus.

#### Tips

• If you have friends in the U.K., pay attention: The definitions of trapezoid and trapezium are flipped in U.K. English. To them, a trapezoid is a four-sided figure with no parallel sides. And in U.K. English, a trapezium is a four-sided figure with two parallel sides.

## How You Talk About a Trapezoid

If you're going to work with trapezoids in math class or talk to somebody who works with them, you need to master a few key pieces of vocabulary. The parallel sides of the trapezoid are called the bases, and when you talk about them one is usually designated as ​a​ and the other as ​b​. (It doesn't matter which is which, as long as you understand which sides you're talking about.)

The right-angle distance between the two bases is called the altitude or height of the trapezoid. You'll need these terms when it comes to operations like finding the area of a trapezoid.

## Finding the Area of a Trapezoid

The formula for finding the area of a trapezoid is

\text{area} = \frac{a + b}{2} × h

where ​a​ and ​b​ are the parallel sides (or bases) of the trapezoid and ​h​ is its altitude, or height. While you can just plug those measurements into the formula and compute it, it might help to think of the process as first averaging the length of the bases, and then multiplying them by the height. It's almost like finding the area of a rectangle (base × height) with one extra step involved.

Example:​ Find the area of a trapezoid with bases that measure 6 feet and 8 feet respectively, and a height of 3 feet. Substituting that information into the formula gives you:

\frac{6 \text{ ft} + 8 \text{ ft}}{2} × 3 \text{ ft} = ?

After working the arithmetic (remember, solve inside the parentheses first) you have:

\begin{aligned} \frac{14 \text{ ft}}{2} × 3 \text{ ft} &=7 \text{ ft} × 3 \text{ ft} \\ &= 21 \text{ ft}^2 \end{aligned}

So the area of your trapezoid is 21 ft2.

## A Special Type of Trapezoid

There's a special type of trapezoid you might learn about in math class: The isosceles trapezoid. This is the shape you get when the angles on each end of a parallel side are equal, and the non-parallel sides are equal in length to each other. Much like an isosceles triangle has special properties, so does an isosceles trapezoid.

When you see this type of shape, you automatically know that the angles on each end of a parallel side are congruent with each other. Or, to put it another way, the lower angles of the isosceles trapezoid are congruent to each other, and the upper angles of the isosceles trapezoid are congruent to each other too.

Finally, the lower base angle of an isosceles trapezoid is supplemental to the upper base angle. That means that if you add the two angles together, they'll equal 180 degrees.

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