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Supplemental Math: Study Aid1 chapters | 19 lessons

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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.

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.'

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.

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

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

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

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.

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

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.

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.

1.) Find the perimeter and area of the following trapezoid:

To find the perimeter, simply add all four sides together.*P* = 12mm + 14mm + 18mm + 13mm = 57mm

To find the area, use the formula *A* = (1/2)(*h*)(*a* + *b*).*A* = (1/2)(11mm)(12mm + 18mm) = 165mm^2

2.) Find the area of the following trapezoid:

Again, use the area formula *A* = (1/2)(*h*)(*a* + *b*).

*A* = (1/2)(6ft)(9ft + 4ft)

*A* = 39ft^2

A **trapezoid** is a 2-dimensional figure with four sides. In order for it to be classified as a trapezoid, it must have at least one set of parallel sides. Trapezoids play a key role in architecture and also can be found in numerous everyday items. Take a look at the glass you are drinking from at your next meal. From the side, it's probably shaped like a trapezoid.

Review the video lesson and its corresponding transcript so that you can:

- Define a trapezoid and identify its properties
- Illustrate several special trapezoids
- Point out the properties of isosceles trapezoids
- Find the perimeter and area of a trapezoid

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Supplemental Math: Study Aid1 chapters | 19 lessons

- Less Than Symbol in Math: Problems & Applications 4:10
- What are 2D Shapes? - Definition & Examples 4:35
- Trapezoid: Definition, Properties & Formulas 3:58
- Using Parentheses in Math: Rules & Examples 3:58
- Universal Set in Math: Definition, Example & Symbol 6:03
- Complement of a Set in Math: Definition & Examples 5:59
- Zero Exponent: Rule, Definition & Examples 4:32
- Quotient Of Powers: Property & Examples 4:58
- What is Simplest Form? - Definition & How to Write Fractions in Simplest Form 5:49
- What is Slope? - Definition & Formulas 7:10
- Skewed Distribution: Examples & Definition 5:09
- Change Of Base Formula: Logarithms & Proof 4:54
- Transformations in Math: Definition & Graph 6:27
- What is Translation in Math? - Definition, Examples, & Terms 4:23
- Fixed Interval: Examples & Definition 4:00
- Scatterplot and Correlation: Definition, Example & Analysis 7:48
- Dilation in Math: Definition & Meaning 5:30
- Simplifying Fractions: Examples & Explanation 4:44
- Go to Overview of Math Concepts

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