A trapezium is a two-dimensional geometrical figure which consists of one pair of sides that are parallel to each other. We can see various real-life examples of the shape of a trapezium, some of which are buckets, suitcases, popcorn boxes, etc. The word ‘trapezium’ has its origin from the word ‘trapeze’, a Greek word, the meaning of which is the table. This two-dimensional geometrical figure can be classified as a quadrilateral whose opposite parallel sides are known as the bases of the trapezium and the other two remaining sides are known as the legs of the trapezium. In this article, we will discuss the area of a trapezium, various types of the trapezium, and also discuss some of the important properties related to the quadrilateral along with solving some examples.

## Area of a Trapezium

The total area that is occupied by a trapezium is known as the area of a trapezium. Calculation of the area of a trapezium is very easy. We can calculate it by obtaining the average of the two bases of the trapezium and then multiplying it with its altitude. To put it in a mathematical manner, we can say that the area of a trapezium is: A = h (x+y) / 2 square units where x and y are the bases of the trapezium and h is the altitude or the height of the trapezium.

## Various Types of Trapeziums

We can classify trapezium into three broad categories which are discussed as follows:

- Right Trapezium: A trapezium is known as a right trapezium when two of its sides have angles equal to 90 degrees that are adjacent to each other.
- Isosceles Trapezium: A trapezium is known as an isosceles trapezium when its two legs are of equal length i.e., one leg of the trapezium is equal to the other leg of the trapezium.
- Scalene Trapezium: A trapezium is known as a scalene trapezium when neither its sides nor its angles are equivalent to each other.

## Various Properties of Trapezium

Each and every geometrical figure has its own set of properties that are unique which helps in the differentiation of the geometrical figure from the rest. The properties help us in understanding the given geometrical figure more vividly. The various properties of a trapezium are as follows:

- It is a two-dimensional geometrical figure.
- The two sides of the trapezium that are parallel to each other are known as the bases of the trapezium.
- Both the diagonals of the trapezium are of equivalent length.
- Trapeziums have diagonals that always intersect each other.
- In a trapezium, all the interior angles sum up to 360 degrees always. This property is common in all the different types of quadrilaterals.

## Some Solved Examples of Trapezium

**Example 1:** Find out the area of a trapezium if its height is 6 units and its bases are 16 units and 14 units respectively.

**Solution:** The area of a trapezium can be given as A = h (x+y) / 2 square units.

Here, x = 16 units, y = 14 units, and h = 6 units.

Thus, area of the given trapezium = h (x+y) / 2 = 6 (16 + 14) / 2= 6 * 15 = 90 square units.

**Example 2:** One of the angles of a right trapezium is 80 degrees. Find out the fourth angle of the right trapezium.

**Solution:** We know that a right angle trapezium has two angles as 90 degrees.

We also know that the sum of all the interior angles of the right trapezium is 360 degrees.

Now, we can conclude that, 90 degrees + 90 degrees + 80 degrees + 4th angle = 360 degree.

Now, the fourth angle of the right trapezium is = 360 degrees – 260 degrees = 100 degrees.

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