The trapezoid is a 2D polygon with an area and perimeter. This is one of the most significant geometrical shapes in math. It can be used in architecture, engineering, and science. Students are taught trapezoid geometry from an early age in order to resolve mathematical problems in fractions of seconds. This article contains in-depth information on trapezoids. Continue reading to find the detailed answer to the question of how many sides does a trapezoid have and its definition, properties, types, and examples.
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Definition Of Trapezoid
The term trapezoid was derived from the Greek word Trapezoin meaning “a little table”. A trapezoid is a convex quadrilateral shape with 1 pair of parallel sides, 4 edges, and 4 vertices. The parallel sides of the trapezoid are known as the bases, and the other sides are known as the legs. Height is defined as the distance between the parallel sides. In some places, the trapezoid is also known as the trapezium. Trapezoids are classified into three types: right, scalene, and isosceles. Because it has 2 opposite parallel sides, a parallelogram is not a trapezoid.
A trapezoid in real life can be a bridge, a table, a handbag, and so on. If both pairs had parallel sides, the trapezoid might have been a parallelogram. It could also have been called a square when both sides were equal in length, or a rectangle when both sides were parallel.
Properties of Trapezoid
These are the characteristics of a trapezoid that distinguish it from other quadrilaterals:
- The bases (top and bottom) are parallel to each other.
- A trapezoid’s opposite sides (isosceles) have the same length.
- Angles adjacent to each other add up to 180°.
- The median will be parallel to both bases.
- The median length can be calculated by the average of both bases. i.e. (a +b)/2
- A parallelogram is formed when both pairs of opposite sides of a trapezoid are parallel.
- A trapezoid can also be considered a square when both pairs of opposite sides are parallel, all sides are equal in length and perpendicular to each other.
- A trapezoid is a rectangle when both pairs of opposite sides are parallel, opposite sides have equal lengths, and opposite sides are perpendicular to each other.
Types of Trapezoids
Trapezoids come in a variety of shapes based on their side and angle measurements. Some examples of common classification are as follows:
- Right Trapezoids
- Isosceles Trapezoids
- Scalene Trapezoids
Isosceles Trapezoid
If the lengths of the trapezoid’s legs or non-parallel sides are equal, the trapezoid is said to be isosceles. The angles of the parallel sides (base) of an isosceles trapezoid have the same measurement. An isosceles trapezoid has a line of symmetry and diagonals that are both the same length.
The trapezoid bases in the isosceles trapezoid ABCD below are AB, and CD. Because AD and BC are not parallel, they are referred to as the trapezoid’s legs.
Scalene Trapezoid
A scalene trapezoid is one in which neither the sides nor the angles of the trapezoid are equal. All 4 sides of the scalene trapezoid above, AB, BC, CD, and DA, have different lengths. The bases, DC and AB, are parallel to one another but differ in length.
Right Trapezoid
A right trapezoid, also known as a right-angled trapezoid, has two right angles. These trapezoids are used to calculate the areas under the curve. There are 2 right angles in the above right trapezoid (or right-angled trapezoid), one at D and the other at A. DC and AB are the only two opposite sides that are parallel to each other.
Trapezoids Formulas
Trapezoids have two major formulas:
- Area of Trapezoid
- Perimeter of Trapezoid
Area of Trapezoid
The trapezoid’s area is determined by taking the average of its parallel sides and multiplying it by its height. To calculate the area of a trapezoid, the lengths of 2 bases and the distance (height) between them must be known. It is the number of unit squares that can fit within the shape and is measured in square units like cm2, m2, in2, and so on. The area (A) of a trapezoid is determined by using its bases, a and b, and its height, h, which is the perpendicular distance between a and b.
As a result, the area of a trapezoid can be calculated using the following formula:
Area =[(AB + CD)/2] × h
A = [(a + b)/2] × h
Where,
- AB and CD = parallel sides
- a = shorter base
- b = longer base
- h = height or altitude
Perimeter of Trapezoid
The perimeter of a trapezoid is described as the total length of the shape’s boundary or the sum of its sides. Because the trapezoid is a two-dimensional shape, the perimeter will also be limited to a two-dimensional plane.
Consider the trapezoid ABCD with side measurements a, b, c, and d shown below. Let’s take a look at the Trapezoid Formula. The perimeter of the trapezoid formula is determined by adding all of the sides together, i.e., AB + BC + CD + DA.
Trapezoid perimeter = sum of all sides = a + b + c + d, where a, b, c, and d are the trapezoid sides.
Real-Life Examples of Trapezoid Shape
Let’s take a look at some real-life examples of Trapezoid Shapes:
- Glass: As you move downward, the width of the glass narrows. As a result, one of the best real-life examples of a trapezoid can be found while looking at the shape of a drinking glass.
- Lamp: Another example of a trapezoid-shaped item in use is a lampshade cap. It is made up of two parallel sides and two non-parallel sides.
- Shovel: The shovel’s blade is shaped like a quadrilateral with two parallel lines and two non-parallel lines. As a result, it is an obvious example of a trapezoid-shaped object in real life.
- Boat: A trapezoid shape can be seen in real life by looking at the base of a paper boat. Some boats in use for water transportation are trapezoidal in shape as well.
- Wheelbarrow: The wheelbarrow’s container is typically trapezoidal in shape. The container’s trapezoid form makes it hold more material than the other shapes.
Examples Of Trapezoid
The trapezoid is used in the following examples:
Example 1: Calculate the area of a trapezoid with 4 and 8-meter bases and a 6-meter height.
Solution: We know that the area of a Trapezoid is 1/2 (a + b)×h
Area = (4 + 8)/2 × 6
Area = 12/2 × 6
= 36 m2
Example 2: A trapezoid has four sides that are 6m, 8m, 4m, and 2m in length. Determine its perimeter.
Solution: We know that the trapezoid perimeter is given by the sum of all the sides.
Therefore, Perimeter = 6 + 8 + 4 + 2
= 20 m
Trapezoid FAQs
Is Trapezoid a Quadrilateral?
Because the trapezoid has 4 sides, it is automatically a quadrilateral. It has 2 parallel sides and 2 non-parallel sides.
What are the Three Attributes of a Trapezoid?
The three primary characteristics of a trapezoid are as follows:
- If the trapezoid is isosceles, its base angles and diagonals are equal.
- The diagonals’ intersection point is collinear (on the same line) with the midpoints of the 2 opposite sides.
- An isosceles trapezoid’s opposite sides are congruent.
Are the Diagonals of a Trapezoid Equal?
Trapezoids are classified into three types: isosceles, scalene, and right. The diagonals of the isosceles trapezoid are equal because the non-parallel or trapezoid legs have the same length. The diagonals of the scalene and right trapezoid are not equal.
Is a trapezoid a parallelogram?
A trapezoid has two competing definitions. A trapezoid isn’t a parallelogram when it is defined as a quadrilateral with exactly 1 set of parallel lines. If a trapezoid is defined as a quadrilateral with at least 1 set of parallel sides, it will become a parallelogram if the quadrilateral has 2 sets of parallel sides
How do you identify a trapezoid?
A trapezoid has to have 4 sides and 1 parallel set of sides. If the quadrilateral has two sets of parallel sides, it is a parallelogram.
Hope that with the above information, you can find the best way to help your kids grasp the answer to the question “what is a trapezoid?” as well as understand all the necessary properties of this geometric shape.
