How to Find the Altitude of a Trapezoid

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  • 0:00 Altitude of a Trapezoid
  • 0:24 Geometric Example
  • 1:42 Tip
  • 2:04 Real-World Example
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Lesson Transcript
Instructor: Maria Airth

Maria has a Doctorate of Education and over 20 years of experience teaching psychology and math related courses at the university level.

In this video, you'll find step-by-step instructions for finding the altitude of a trapezoid. You'll also learn how to use these same steps to find the length of a leg of a trapezoid given the altitude.

Altitude of a Trapezoid

A trapezoid is a four-sided shape with two parallel sides, called the base and the top. The non-parallel sides are referred to as legs. The altitude is the distance between the base (bottom) and the top of the trapezoid. The altitude of a trapezoid is simply its height.

Geometric Example

Let's see how we can calculate the altitude of a trapezoid using an example:


Altitude of Trapezoid


Step 1:

We'll begin by drawing a line from the vertex at the top of the trapezoid to the base to create a right triangle, or a triangle with a 90 degree angle.


Altitude of Trapezoid Step 1


Step 2:

Next, we'll calculate the base of the triangle we just drew. This example is an isosceles triangle, because it has two equal sides. In this example, the base of the trapezoid (14 inches) is equal to the top of the trapezoid (6 inches) plus two times the bases of the right triangles (x).

In algebraic terms, 14 = 6 + 2x.


Altitude of Trapezoid Step 2


Step 3:

Now we'll use the Pythagorean Theorem to calculate the altitude, or one leg of the right triangle.


Altitude of Trapezoid Step 3


Step 4:

Finally, we'll format our answer according to the original problem. The altitude of this trapezoid is 3 inches.

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