Trapezoid – Definition, Types, Properties, Examples, FAQs

What is Trapezoid?

A trapezoid, also known as a trapezium, is a flat closed shape having 4 straight sides, with one pair of parallel sides. 

The parallel sides of a trapezium are known as the bases, and its non-parallel sides are called legs. The parallel sides can be horizontal, vertical or slanting. 

The perpendicular distance between the parallel sides is called the altitude. 

Examples:

Non-Examples:

(A) It is not a trapezoid because it is a 6-sided figure.

(B) It is not a trapezoid because it is a 3-sided figure with no parallel sides.

(C) It is not a trapezoid because it is a curved figure.

(D) It is not a trapezoid because it has rounded corners and 2 pairs of parallel sides.

Trapezoid Definition

• Exclusive Definition: A trapezoid is a quadrilateral with exactly one pair of parallel sides. (By this definition, a parallelogram is not a trapezoid since it has two pairs of parallel sides.)
  
• Inclusive Definition: A trapezoid is a quadrilateral with at least one pair of parallel sides. (By this definition, a parallelogram becomes a special type of trapezoid, a trapezoid with two pairs of parallel sides.)
  

Types of Trapezoid

Trapezoid is of three types namely

1. Right trapezoid: It has a pair of right angles.

2. Isosceles trapezoid: It has equal length of non-parallel sides. In the image, sides, AD and BC are equal.

3. Scalene trapezoid: It neither has equal angles nor has equal sides.

Median of Trapezoid

A median of a trapezoid is the line segment joining the midpoints of the two non-parallel sides of a trapezoid.

The median of a trapezoid is parallel to the set of parallel lines.

Median = $\frac{BC+AD}{2}$ = $\frac{a+b}{2}$

Properties of a Trapezoid

• The bases are parallel to each other.
• The median is parallel to both the bases and its length will be the average of the length of the bases.
• Sum of all the angles in a trapezoid is equal to 360°.
• The sum of the angles on the same side is equal to 180°.

Area of Trapezoid

Area of a trapezoid = $\frac{1}{2}$ × (sum of parallel sides) × (distance between them)

Let ABCD be a trapezoid in which AB is parallel to DC and let h be the height.

Area = $\left\{\frac{1}{2}\times (AB + BC)\times h \right\}$

= $\left\{\frac{1}{2}\times (a + b)\times h \right\}$

Perimeter of Trapezoid

The perimeter of a trapezoid is the sum of all its sides.

Therefore, for the trapezoid shown above with sides AB, BC, CD and DA, the perimeter can be written as

Perimeter = AB + BC + CD + DA

Real Life Examples

We can find trapezoids in many real-life objects For example a lamp, popcorn box, handbag, and so on.

Solved Examples on Trapezoid

Example 1: Fill in the blanks.

1. The trapezoid having non-parallel sides equal is known as ______________.
2. _____________ trapezoid has a pair of adjacent angles equal to 90°.
3. Neither the sides nor the angles of _______________ trapezoid are equal.

Solution:

1. isosceles trapezoid
2. Right
3. scalene

Example 2: Find the length of median PQ of given trapezoid.

Solution:

Median = $\frac{1}{2}\times (\text{sum of the basis}) = \frac{AD + BC}{2} = \frac{8 + 30}{2} cm = 19 cm$

Example 3: Find the perimeter of a given trapezoid.

Solution:

Perimeter = PQ + QR + RS + SP = (15 + 6 + 20 + 5) cm = 46 cm

Example 4: Find the area of a given trapezoid.

Solution:

Area = $\frac{1}{2}\times (\text{sum of parallel sides})\times (\text{altitude})$

= $\frac{1}{2}\times (7 + 11)\times 6$ sq.cm

= $\frac{1}{2}\times 18\times 6 sq.cm$

= 54 sq.cm

Practice Problems On Trapezoid

Frequently Asked Questions On Trapezoid