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Trapezoid: Definition, Properties & Formulas

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  • 0:02 Definition of a Trapezoid
  • 0:26 Special Trapezoids
  • 1:28 Properties of a Trapezoid
  • 2:26 Practice
  • 3:30 Lesson Summary
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Lesson Transcript
Instructor: Jennifer Beddoe
A trapezoid has one pair of parallel sides. Learn more about the properties and formulas of trapezoids in this lesson. A quiz following the lesson will allow you to solidify what you've learned.

Definition of a Trapezoid

Image of a trapezoid
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A trapezoid is a 2-dimensional geometric figure with four sides, at least one set of which are parallel. The parallel sides are called the bases, while the other sides are called the legs. The term 'trapezium,' from which we got our word trapezoid has been in use in the English language since the 1500s and is from the Latin meaning 'little table.'

Special Trapezoids

There are a few special trapezoids that are worth mentioning.

In an isosceles trapezoid, the legs have the same length and the base angles have the same measure.

Isosceles trapezoid
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In a right trapezoid, two adjacent angles are right angles.

Right trapezoid
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If the trapezoid has no sides of equal measure, it is called a scalene trapezoid.

Scalene trapezoid
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A parallelogram is a trapezoid with two sets of parallel sides.

Parallelogram
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There is actually some controversy over whether a parallelogram is a trapezoid. One group states that the definition of a trapezoid is having only one set of parallel sides, which would exclude the parallelogram because it has two sets of parallel sides. The other, more mainstream group, states that the definition of a trapezoid is having at least one set of parallel sides, which includes the parallelogram. For our discussions, because it is the more widely accepted view, we will consider a parallelogram to be a trapezoid.

Properties of a Trapezoid

The formula for the perimeter of a trapezoid is P = (a + b + c + d). To find the perimeter of a trapezoid, just add the lengths of all four sides together.

The formula for the area of a trapezoid is A = (1/2)(h)(a + b), where:

  • h = height (This is the perpendicular height, not the length of the legs.)
  • a = the short base
  • b = the long base

Dimensions of a trapezoid
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An isosceles trapezoid has special properties that do not apply to any of the other trapezoids:

  • Opposite sides of an isosceles trapezoid are the same length (congruent).
  • The angles on either side of the bases are the same size or measure (also congruent).
  • The diagonals are congruent.
  • Adjacent angles (next to each other) along the sides are supplementary. This means that their measures add up to 180 degrees.

Practice

Let's try a couple of practice problems to test your newfound trapezoid knowledge. Feel free to pause the video at any point to work through the problems yourself.

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