Question

The area of a trapezium is 180 sq. cm and its height is 9 cm. If one of the parallel sides is longer than the other by 6 cm, find the length of the parallel sides. ​

Answer 1

Height of trapezium =9 cm

one of other side of trapezium is longer than 6 cm

one is 6cm and other is x+6

Area of trapezium =

1÷2 (sum of parallel sides )×height

1÷2 ( x + x+6) ×9 =180

1÷2 (2x+6)×9= 180

x+3×9=180

x+3=180÷9

x+3=20

x=20-3

x=17

one side is x = 17 cm

other side x+6 =17+6=23cm

Answer 2

Given :

• The area of a trapezium is 180 cm².

• The height of a trapezium = 9 cm.

• One of the parallel sides is longer than the other by 6 cm.

To find :

• The length of the parallel sides =?

Step-by-step explanation :

Let the one parallel side be x.

And, another parallel side be ( x + 6 ).

We know that,

Area of trapezium = 1 / 2 × ( sum of parallel sides ) × height of the trapezium

Substituting the values in the above formula, we get,

➮ 180 = 1 / 2 × ( x + x + 6 ) × 9

➮ 180 = 9 ( 2x + 6 ) / 2

➮ 9 ( 2x + 6 ) = 180 × 2

➮ 18x + 54 = 360

➮ 18x = 360 - 54

➮ 18x = 306

➮ x = 306 / 18

➮ x = 17 cm.

Therefore, We know that value of x = 17 cm

Hence,

One parallel side of trapezium = x = 17 cm.

And, another parallel side of trapezium = x + 6 = 23 cm