Trapezoid

The trapezoid is fascinating because it is defined based on the geography you belong to. If you’re visiting the United Kingdom on an exchange trip and ask a student to draw a trapezoid for you, then they will draw it like a trapezium. A trapezoid is also called a trapezium in some parts of the world and it is a type of quadrilateral with one pair of opposite sides parallel to each other.

A trapezoid is a four-sided closed 2D figure which has an area and its perimeter. Two sides of a trapezoid are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid. The shortest distance between two parallel sides is known as the altitude. Since the opposite sides are parallel to each other, calculating the area of a trapezoid is simple. 

These are the properties of a trapezoid that make it stand out from other quadrilaterals:

• The bases (the top and bottom) are parallel to each other
• Opposite sides of a trapezoid (isosceles) are of the same length
• Angles next to each other sum up to 180°
• The median is parallel to both the bases
• Median's length is the average of both the bases i.e. (a +b)/2 
• If both pairs of the opposite sides are parallel in a trapezoid, it is considered a parallelogram 
• If both pairs of the opposite sides are parallel, all sides are of equal length, and at right angles to each other, then a trapezoid can be considered as a square
• If both pairs of the opposite sides are parallel, its opposite sides are of equal length and at right angles to each other, then a trapezoid can be considered as a rectangle 

There are three types of trapezoids, and those are given below:

1. Isosceles Trapezoid
2. Scalene Trapezoid
3. Right Trapezoid

Isosceles Trapezoid: If the legs or non-parallel sides of the trapezoid are equal in length, then it is called an isosceles trapezoid. The angles of the parallel sides (base) in the isosceles trapezoid are equal to each other. An isosceles trapezoid has a line of symmetry and both the diagonals are equal in length. 

In the below isosceles trapezoid XYZW, XY and WZ are called the bases of the trapezoid. WX and YZ are called the legs of the trapezoid since they are not parallel to each other. 

Scalene Trapezoid: When neither the sides nor the angles of the trapezoid are equal, then it is a scalene trapezoid. In the below scalene trapezoid, all four sides i.e. AB, BC, CD, and DA are of different lengths. The bases i.e. DC and AB are parallel to each other but are of different lengths.

Right Trapezoid: A right trapezoid also called the right-angled trapezoid, has a pair of right angles. These kinds of trapezoids are used to estimate the areas under the curve. In the below right trapezoid or right-angled trapezoid, there are two right angles one at D and the other one at A. One pair of opposite sides i.e. DC and AB are parallel to each other. 

The area of the trapezoid is calculated by measuring the average of the parallel sides and multiplying it with its height.

The area of a trapezoid is calculated by the following formula:

Area =[(AB + CD)/2] x h

Where AB and CD are the parallel sides and h is the height

The perimeter of a trapezoid is the sum of all its sides. If A, B, C, D are the four sides of a trapezoid, then the perimeter formula is: 

Perimeter = AB + BC + CD + AD

Related Topics on Trapezoid

Listed below are a few topics that are related to a trapezoid.

• Quadrilaterals 
• Area 
• Perimeter 
• Geometric shapes 
• Shapes
• Square
• Rectangle

What are Trapezoids?

A trapezoid is a four-sided closed 2D shape that has an area and a perimeter. It is also called a Trapezium. The sides of a trapezoid are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid. The shortest distance between two parallel sides is known as the altitude.

How to Find the Area of a Trapezoid?

The area of a trapezoid is calculated by calculating the average of the two parallel sides and multiplying it by its height.

Area = [(a + b)/2] x h, where a and b are the lengths of the bases and h represents the height.

What is the Equation for a Trapezoid?

There are two equations for a trapezoid. One equation calculates its area; the other its perimeter. The perimeter of a trapezoid PQRS is given as, Perimeter = PQ + QR + RS + PS. The area of a trapezoid = [(a + b)/2] x h, where a and b are the lengths of the bases and h represents the height.

Is Trapezoid a Quadrilateral?

Since the trapezoid has four sides, it automatically becomes a quadrilateral. It has two sides that are parallel, and two sides that aren’t.

What are the Three Attributes of a Trapezoid?

The three main attributes of a trapezoid are as follows

1. Its base angles and diagonals are equal if the trapezoid is isosceles
2. The intersection point of the diagonals is collinear (in the same line) to the midpoints of the two opposite sides
3. Opposite sides of an isosceles trapezoid are congruent

How do you Find the Missing Side of a Trapezoid?

The missing side of the trapezoid can be determined from the information given to you. In case, you have the area, and the length of the bases, you can find the length of the height. You can also determine the length of the missing side if you know the perimeter and the length of the other three sides of the trapezoid.

Are the Diagonals of a Trapezoid Equal?

Trapezoid are of three kinds - Isosceles, Scalene, and Right. In the case of the isosceles trapezoid, the diagonals are equal since the non-parallel or the legs of the trapezoid are equal in length. In the case of scalene and right trapezoid, diagonals are not equal.