The Trapezoid

In the world of quadrilaterals, the formula to find area of Trapezoids is one of the most feared by middle school students. Perhaps it’s the use of parentheses. If you throw these bad boys into a problem it’s sure to create a certain level of anarchy. Possibly it’s the use of the numbers 1 and 2 written below and to the right of the two bases (b) in the parentheses.

Regardless of of the reason, the formula for Area of Trapezoids has caused many kids to surrender without so much as a fight.

The kicker is that the formula is not difficult to solve. In this blog we will look at a couple of the key terms, dissect the formula, give three examples of finding area and show you a few ways to model finding the area.

Key Terms

There are two key terms in the world of the Trapezoid: Bases and Height.

The Bases are two sides that are parallel. Trapezoids have only one set of parallel sides. The Height can also be thought of as the distance between the bases. In most examples, the two bases are on the top and the bottom, but if you rotate the trapezoid 90 degrees the bases are now on the right and left sides.

Area of Trapezoid Formula

There are two common formulas that you will see used when finding the area of a trapezoid:

Area = 1/2 (Base 1 + Base 2) x height or

Area = (Base 1 + Base 2) divided by 2 x height

It’s important to understand that dividing by 2 and multiplying by 1/2 are the same thing. For example, 10 divided by 2 equals 5 and 10 times 1/2 also equals 5.

What is helpful to understand is that 1/2 (Base 1 + Base 2) and (Base 1 + Base 2) divided by 2 are both just ways of finding the average of the two bases. You can think of this as the Mean or the Median it doesn’t matter. So really Area of a Trapezoid is just the Average of the Bases x Height (or the distance between the bases)

3 Examples of Finding area of Trapezoids

3 Ways to model Finding the area of Trapezoids

Example #1

This is an example of a Trapezoid when the “triangles” are the same on both sides.

Example #2

This is an example of a trapezoid with two right angles. As a result there is only one “triangle.”

Example #3

This an example of a trapezoid with triangles on each side, but both have a different base.

Watch the Video !

Check out: Finding the Area of Unique Shapes.

A collection of 44 different Shapes using triangles, quadrilaterals (including trapezoids) and circles.