As per the Euclidean geometry, a quadrilateral that has one pair of parallel opposite sides is known as a trapezium. The word trapezium originated from the Greek word "trapeza" which means table. In this lesson, we will learn more about the properties of trapezium using examples. Stay tuned to learn more about trapezium and its properties!!!
|1.||What is a Trapezium?|
|2.||Types of Trapeziums|
|3.||Properties of Trapezium|
|4.||Area and Perimeter of Trapezium|
|5.||Solved Examples on Trapezium|
|6.||Practice Questions on Trapezium|
|7.||FAQs on Trapezium|
What is a Trapezium?
A trapezium is a two-dimensional quadrilateral (as it is made of four straight lines) having a pair of parallel opposite sides. The parallel opposite sides are referred to as the base and the nonparallel sides are referred to as legs of the trapezium. It is a closed plane shape having four sides and four corners. A trapezium shape is represented as:
In the above figure, XY and WZ are the bases of the trapezium while XW and YZ are the legs of the trapezium. Trapezium shape can be observed in the objects around us, like
Types of Trapeziums
Trapeziums can be classified as :
- Isosceles Trapezium
- Scalene Trapezium
- Right Trapezium
Trapeziums are classified on the basis of the length of legs or the measurement of their angles. The definition of each type of trapezium along with its shape is:
Properties of Trapezium
Every quadrilateral has its own properties which make it identifiable and different from the rest. These properties give more insights into the geometrical construction of a shape. Thus, the properties of a trapezium are:
- The bases of a trapezium(isosceles) are parallel to each other.
- The length of both the diagonals is equal.
- The diagonals of a trapezium always intersect each other.
- The adjacent interior angles in a trapezium sum up to be 180°.
- The sum of all the interior angles in a trapezium is always 360°.
Area and Perimeter of Trapezium
Let us take a trapezium having the lengths of parallel sides a, b units respectively and the altitude "h".
The area of trapezium is given by calculating the average of bases and multiplying its result to the altitude.
Hence, area of trapezium = ((AB + DC)/2) × AM =((a+b)/2) × h where AB, CD show the bases and AM is the altitude.
The perimeter of a trapezium is given by taking the sum of all its sides.
Hence, perimeter of trapezium = AB + BC + CD + AD
Topics Related to Trapezium
Solved Examples on Trapezium
Example 1: Determine the value of the area for a trapezium if the length of its bases is 13 units, 15 units respectively, and height 4 units.
Solution: As we know, the area of trapezium is ((a+b)/2) × h. Here, a = 13 units, b = 15 units and h = 4 units. Hence, area of trapezium = ((a+b)/2) × h = ((13+15)/2) × 4 ⇒ area of trapezium = 14 × 4 = 56 units2. Therefore, the area of trapezium is 56 units2 .
Example 2: Find the fourth angle of the right trapezium if one of the given angles is 60°.
Solution: As we know, the right angles in a right trapezium are in a pair and the sum of all the interior angles in a trapezium is always 360°.Thus, two angles measure 90°. If one of the given angles is 60° and the angle to be calculated is x°. The fourth angle of trapezium can be calculated as, x° + 90° + 90° + 60° = 360° ⇒ x°= 360° - (90° + 90° + 60°) = 120°. Therefore, the fourth angle of the right trapezium is 120°.
Example 3: Find the length of one side of trapezium, if the rest three sides measure 10 units, 12 units, 7 units, and perimeter is 40 units.
Solution: As we know, the perimeter of a trapezium is given as the sum of all its sides. Let the length to be found is l units.Thus, the perimeter = 40 = 10 + 12 + 7 + l ⇒ l = 40 - (10 + 12 + 7) = 11 units. Therefore, the length of one side of trapezium is 11 units.
FAQs on Trapezium
What is a Trapezium Shape?
A two-dimensional quadrilateral that has a pair of parallel sides is referred to as a trapezium shape.
How Do You Find the Area of a Trapezium?
The area of a trapezium is found by calculating the average of bases and multiplying its result to the altitude, that is, ((a+b)/2) × h.
Is Trapezium a Quadrilateral?
Yes, trapezium is a quadrilateral.
Does a Trapezium Have Parallel Sides?
Yes, the trapezium has a pair of parallel sides which are referred to as the base.
Can a Trapezium have a right angle?
Yes, a trapezium can have a right angle. A trapezium with a pair of right angles is known as a right trapezium.
What are the Properties of a Trapezium?
The properties of a trapezium are:
- The bases of a trapezium are always parallel to each other.
- Both the diagonals have the same length and they always intersect each other.
- The sum of adjacent interior angles of a trapezium is 180°.
- The interior angles in a trapezium always sum up to 360°.