**Area of Trapezium: **Trapezium is a wide shape. Various formulas are used to calculate the area of a trapezium. In this article, we will consider different methods of determining the area of a trapezoid and understand its importance.

## What is a trapezium?

A trapezium is a four-sided shape with one set of parallel sides. The parallel sides are called the bases of the trapezium, and the non-parallel sides are called legs. The height of a trapezium is the perpendicular distance between the bases. The area of a trapezium is equal to the average of the bases multiplied by the height.

Trapezoids are a common shape in nature and everyday life. For example, the wings of a butterfly, the roof of a house, and the teeth of a saw are all trapezoids. Trapezoids are also used in many different structures and machines, such as bridges, airplanes, and cars.

**Area Of Trapezium: Definition**

A trapezium is a 2D shape, it is a quadrilateral and has 4 sides out of which 2 sides are parallel to each other. The area of a trapezium is equal to the sum of the areas of two triangles and the area of the rectangle. A trapezium whose two parallel sides are equal and make equal angles at one base is called isosceles trapezium.

## types of trapezium

Trapezium is divided into 3 distinct sections as given below:

**Isosceles Trapezium:**It can be defined as a trapezium in which both the legs and base angles are of equal measure.**Right Trapezium:**A right trapezium is a trapezium with two right angles.**Scalene Trapezium:**A scalene trapezium is a trapezium whose sides are not of equal measure.

**Area Of Trapezium: Properties**

A quadrilateral with at least one pair of parallel sides is called a trapezoid in American and Canadian English. In British and other forms of English, the trapezoid is called trapezium. Trapezium or trapezium is a quadrilateral in which one pair of opposite sides are parallel to each other and the other pair of trapezium is not parallel. Some properties of a trapezium are listed below:

- The sum of the angles of a trapezium is 360º.
- A trapezium is not a parallelogram (because in a trapezium only one pair of opposite sides is parallel and we need both pairs of sides to be parallel in a parallelogram).
- A trapezium has 4 sides unequal unless it is an isosceles trapezium in which 2 parallel sides are equal.
- The diagonals of a trapezium bisect each other.
- The sum of two pairs of adjacent angles of a trapezium adds up to 180º.

**Area Of Trapezium Formula**

To calculate the area of a trapezium, you need to draw a perpendicular between two parallel lines. The height of the perpendicular will be denoted as 'h' which is the distance between the parallel sides.

Therefore, the area of a trapezium can be calculated from the formula given below:

**Area of trapezium = ****1/2 x ****distance between parallel sides x parallel ****arms ****sum of**

**Area of trapezium =**

**1/2 x**

**distance between parallel sides x parallel**

**arms**

**sum of**

**Area ****= 1/2xhx (AB + DC)**

**Area**

**= 1/2xhx (AB + DC)**

**Questions based on area of trapezium (Area of Trapezium Examples)**

**Example 1: The lengths of two parallel sides of a trapezium are given in the ratio 3:2 and the distance between them is 8 cm. If the area of the trapezium is 400 square cm, find the length of the parallel sides.**

Solution: Suppose, two parallel sides 3x and 2x are given.

*So area of trapezium = 1/2 x distance between parallel sides x sum of parallel sides*

400= 1/2 x (3x + 2x) x 8

400 = 1/2 x 5x x 8

400 = 20x => x = 20 cm

**The lengths of the parallel sides are 60 cm and 40 cm.**

**Q2. The lengths of two parallel sides of a trapezium are 27 cm and 19 cm respectively, and the distance between them is 14 cm. Find the area of the trapezium.****Plough:**

Area of trapezium = 1/2 x distance between parallel sides x sum of parallel sides

Area of trapezium = {¹/₂ × (27 + 19) × 14} cm² = 322 cm²**Q3.**** The area of a trapezium is 352 cm² and the distance between its parallel sides is 16 cm. If the length of one of the parallel sides is 25 cm, find the length of the other side.****Plough: **

Let the length of the required side be x cm.

So area of trapezium = {¹/₂ × (25 + x) × 16} cm²

Area of trapezium = (200 + 8x) cm².

But area of trapezium = 352 cm² (given)

Hence, 200 + 8x = 352

⇒ 8x = (352 – 200)

⇒ 8x = 152

⇒ x = (152/8)

⇒ x = 19.

The length of the other side is 19 cm.

**Q4. What is the area of a trapezium when the bases are 12 cm and 20 cm respectively and the distance between two parallel sides is 10 cm?**

**Plough:** Has been given,

a = 12 cm

b = 20 cm

Distance between two parallel sides, h = 10 cm

Area of trapezium = 1/2 (12 + 20) 10

= 160 cm²

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