Definition, formula and questions based on it

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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:

  1. The sum of the angles of a trapezium is 360º.
  2. 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).
  3. A trapezium has 4 sides unequal unless it is an isosceles trapezium in which 2 parallel sides are equal.
  4. The diagonals of a trapezium bisect each other.
  5. 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 = 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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