If you have been or are currently a student of geometry, then it is quite likely that you have come across the term “trapezoid”. If the word itself is not familiar to you, you may be scratching your head right now as to what it means!
Well, in this article, I will help you better understand this geometry term by giving you a definition of a trapezoid and explaining what you need to know to identify one. We will also look at some of the different types of trapezoids and other related geometrical figures. So, let’s get started!
What is a Trapezoid?
Simply put, a trapezoid is a four-sided geometrical figure that has only one pair of parallel sides. Additionally, the parallel sides are called the bases of the trapezoid. The other two non-parallel sides are called the legs of the trapezoid. Here is a picture of a trapezoid to help you visualize the shape better:
| A Trapezoid | |
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As shown in the picture above, the height of a trapezoid is the perpendicular distance between the parallel bases. This is an important dimension of the trapezoid that comes into play when calculating various properties of the shape.
Identifying a Trapezoid
Now that you know what a trapezoid looks like, you may be wondering how to identify one. Well, here are the basic conditions for identifying whether a four-sided figure is a trapezoid:
One Pair of Parallel Sides
As mentioned earlier, a trapezoid has only one pair of parallel sides. This means that the other two sides are not parallel and therefore do not have the same length nor are they parallel to each other.
No Right Angles
A trapezoid can have different angles; however, it does not have any right angles. This means that the two non-parallel sides will always have an acute or obtuse angle between them.
Same Side Interior Angles Add up to 180 Degrees
Another way to identify a trapezoid is by observing its angles. If we take one of the bases and one of the legs, then we can see that the sum of the two same-side interior angles adds up to 180 degrees. This is because those angles are supplementary (meaning they add up to 180 degrees).
Types of Trapezoids
There are different types of trapezoids depending on the lengths of their sides and angles. Let’s take a look at some of these types below.
Isosceles Trapezoid
An isosceles trapezoid is a trapezoid where the non-parallel sides have the same length. This means that the angles between the non-parallel sides and a base are equal. Here is an example of an isosceles trapezoid:
| An Isosceles Trapezoid | |
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Right Trapezoid
A right trapezoid is a trapezoid where one of the angles between the non-parallel sides and a base is a right angle (90 degrees). In other words, a right trapezoid has one right angle. Here is an example of a right trapezoid:
| A Right Trapezoid | |
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Scalene Trapezoid
A scalene trapezoid is a trapezoid where none of the sides and angles are equal. In other words, a scalene trapezoid has no congruent sides or angles. Here is an example of a scalene trapezoid:
| A Scalene Trapezoid | |
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Calculating Various Properties of a Trapezoid
Now that we have a good understanding of what a trapezoid is and the different types of trapezoids, let’s take a look at some of the properties of a trapezoid that we can calculate.
Area of a Trapezoid
The area of a trapezoid is given by the formula: A = (a+b)h/2, where a and b are the two parallel bases, and h is the height (perpendicular distance between the bases).
Perimeter of a Trapezoid
The perimeter of a trapezoid is simply the sum of the lengths of all its sides. This can be calculated as: P = a+b+c+d, where a and b are the parallel bases, and c and d are the non-parallel legs.
Height of a Trapezoid
The height of a trapezoid is the perpendicular distance between the two parallel bases. This can be calculated using the Pythagorean theorem or by using the formula: h = |(b-a)/2|sin(α), where a and b are the parallel bases and α is the acute angle between a base and a leg.
Angle Between Legs of a Trapezoid
The angle between the legs of a trapezoid can be calculated using the formula: θ = tan-1((d-c)/h), where c and d are the non-parallel legs, and h is the height of the trapezoid.
Trapezoid vs. Other Geometrical Figures
It is important to understand the differences between a trapezoid and other geometrical figures that may appear similar, but are, in fact, different.
Trapezoid vs. Parallelogram
A parallelogram is a four-sided figure where both pairs of opposite sides are parallel to each other. While a parallelogram may look similar to a trapezoid, they are different shapes because a parallelogram has two pairs of parallel sides whereas a trapezoid only has one pair of parallel sides.
Trapezoid vs. Kite
A kite is a four-sided figure where two pairs of adjacent sides are of equal length. While a kite can look like a trapezoid, they are different shapes because a kite does not have any parallel sides.
Conclusion
In conclusion, trapezoids are four-sided figures with only one pair of parallel sides. The other two sides are called legs. The height of the trapezoid is the perpendicular distance between the parallel base sides. Trapezoids can be classified into different types based on the angles and lengths of their sides. Different properties of trapezoids, including their area, perimeter, height, and angle between legs, can be calculated using various formulas. Finally, it is important to be able to differentiate between trapezoids and other geometrical shapes such as parallelograms and kites.
Common Questions and Their Answers
- Q: How many pairs of parallel sides does a trapezoid have?
- A: A trapezoid has only one pair of parallel sides.
- Q: Can a trapezoid have two right angles?
- A: No, a trapezoid cannot have two right angles. This is because a trapezoid can only have acute or obtuse angles.
- Q: What is the formula for calculating the area of a trapezoid?
- A: The area of a trapezoid is given by the formula: A = (a+b)h/2, where a and b are the two parallel bases, and h is the height (perpendicular distance between the bases).
- Q: What is the angle between the legs of a trapezoid?
- A: The angle between the legs of a trapezoid can be calculated using the formula: θ = tan-1((d-c)/h), where c and d are the non-parallel legs, and h is the height of the trapezoid.
- Q: Can a trapezoid be an isosceles triangle?
- A: No, a trapezoid cannot be an isosceles triangle since the definition of an isosceles triangle requires only two sides to be of equal length, while a trapezoid has four sides.
References
Here are a few references used in this article:
- “Trapezoid – Math Open Reference.” Math Open Reference, https://www.mathopenref.com/trapezoid.html. Accessed 20 Oct. 2021.
- “Trapezoid – Wikipedia.” Wikipedia, https://en.wikipedia.org/wiki/Trapezoid. Accessed 20 Oct. 2021.
- “Geometry Definitions: Trapezoid (Isosceles, Scalene) & Properties.” SplashLearn, https://www.splashlearn.com/math-vocabulary/geometry/trapezoid. Accessed 20 Oct. 2021.