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.
|1.||What is a Trapezium?|
|2.||Types of Trapezium|
|3.||Properties of Trapezium|
|4.||Area and Perimeter of Trapezium|
|5.||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 opposite parallel sides are referred to as the base and the non-parallel 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 while XW and YZ are the legs of the trapezium. Trapezium shape can be observed in the objects around us, like:
Types of Trapezium
There are mainly three types of trapezium which are given below:
- 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 given below.
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. The trapezium properties are listed below:
- It is a 2D shape.
- The bases of a trapezium 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 sum up to 180°.
- The sum of all the interior angles in a trapezium is always 360°.
Trapezium Area and Perimeter
Let us take a trapezium having the lengths of parallel sides a, b units respectively and the altitude "h".
The trapezium area 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 ABCD = AB + BC + CD + AD.
Topics Related to Trapezium
Check these interesting articles related to the concept of trapezium shape in geometry.
Example 1: Determine the area of a trapezium if the length of its bases is 13 units, and 15 units respectively, and height is 4 units.
Solution: As we know, the trapezium area formula is ((a+b)/2) × h. Here, a = 13 units, b = 15 units and h = 4 units. Hence, area = ((a+b)/2) × h = ((13+15)/2) × 4 ⇒ 14 × 4 = 56 units2. Therefore, the required area 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, in a right trapezium the right angles are in a pair and the sum of all the interior angles in a trapezium is always 360°. Thus, two angles measure 90° each. If one of the given angles is 60°, let the angle to be calculated be x°. The fourth angle can be calculated as x° + 90° + 90° + 60° = 360°.
⇒ x° = 360° - (90° + 90° + 60°) = 120°. Therefore, the measure of the fourth angle is 120°.
Example 3: Find the length of the fourth side of the trapezium, if the rest three sides measure 10 units, 12 units, and 7 units, and the perimeter is 40 units.
Solution: As we know, the trapezium perimeter is given as the sum of all its sides. Let the length to be found is 'a' units. Thus, the perimeter is 40 = 10 + 12 + 7 + a.
⇒ a = 40 - (10 + 12 + 7) = 11 units. Therefore, the length of the fourth side is 11 units.
FAQs on Trapezium
What is a Trapezium Shape?
A two-dimensional quadrilateral that has a pair of non-adjacent parallel sides and a pair of non-parallel sides is referred to as a trapezium shape. It looks like a triangle that is cut from the top.
How do you find the Area of a Trapezium?
The area of a trapezium can be found by calculating the average of bases and multiplying the result to the altitude, that is, ((a+b)/2) × h, where a and b are the lengths of the parallel sides and h is the height of the trapezium.
Is Trapezium a Quadrilateral?
Yes, trapezium is a quadrilateral. It has four sides, four vertices, and four angles. The sum of all four interior angles of a trapezium is 360 degrees.
Does a Trapezium Have Parallel Sides?
Yes, the trapezium has a pair of parallel sides which are referred to as the bases.
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 given below:
- The bases are always parallel to each other.
- Both the diagonals 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°.
What is the Formula of Area of Trapezium?
If 'h' is the height and a and b are the lengths of the parallel sides of the trapezium, the trapezium area formula is given as 1/2 × (a + b) × h square units.
What is Isosceles Trapezium?
An isosceles trapezium is the one in which both the legs or the non-parallel sides are equal to each other. The angles opposite to those two equal sides are also equal.
What is the Difference Between Trapezium and Trapezoid?
Both trapezium and trapezoid mean the same. They refer to a four-sided polygon having a pair of non-adjacent parallel sides and a pair of non-adjacent non-parallel sides. Generally, the trapezium is as per UK English and trapezoid is a common term in US English.