Area Of Trapezium: Definition, Properties, Formula And Examples

Area of Trapezium: Trapezium is a 2-dimensional geometric shape with 4 sides and 4 vertexes. It has at least one pair of parallel sides. in order to calculate the area of a trapezium, one must apply the appropriate formula to calculate the area of trapezium. This post comprises of the definition, properties, formula with examples of a trapezium to explain the students on the applications of the same.

Area Of Trapezium: Properties

Some of the 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 (as only one pair of opposite sides is parallel in a trapezium and we require both pairs to be parallel in a parallelogram).
3. The 4 sides of a trapezium are unequal unless it is an isosceles trapezium in which the 2 parallel sides are equal.
4. The diagonals of a trapezium bisect each other.
5. Two pairs of adjacent angles of a trapezium sum up to 180 degrees.

The formula of the Area Of Trapezium

In order to calculate the area of a trapezium, you need to draw a perpendicular between the two parallel lines. The perpendicular will be donated as the height ‘h’ which is the distance between the parallel sides.

Hence, the area of a trapezium is given by the formula:

Area of Trapezium = 1/2 x distance between the parallel sides x Sum of parallel sides

Area = 1/2 x h x (AB + DC)

Area Of Trapezium Examples 

Q1: The length of the 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 trapezium is 400 cm², find the length of the parallel sides.

Solution:

Let the 2 parallel sides as 3x and 2x.

Then, as the area of trapezium is 1/2 x distance between the 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 length of the parallel sides are 60 cm and 40 cm.

Q2. Two parallel sides of a trapezium are of lengths 27 cm and 19 cm respectively, and the distance between them is 14 cm. Find the area of the trapezium.

Solution:

Area of the trapezium = ¹/₂ × (sum of parallel sides) × (distance between them)

Area of the 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 one of the parallel sides is of length 25 cm, find the length of the other.

Solution: 

Let the length of the required side be x cm.

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

Area of the trapezium = (200 + 8x) cm².

But, the area of the trapezium = 352 cm² (given)

Therefore, 200 + 8x = 352

                ⇒ 8x = (352 – 200)

⇒ 8x = 152

⇒ x = (152/8)

⇒ x = 19.

The length of the other side is 19 cm.