Question

The area of a trapezium is 180cm square and it's height is 9cm.If one of the parallel sides is longer than the other by 6cm, find the two parallel sides.

Answer 1

Step-by-step explanation:

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

Question :-

The area of the Trapezium is 180 cm² and it's height is 9cm . If one of the parallel sides is longer than the other by 6 cm . Find the two parallel sides

Answer :-

Given :-

The area of the Trapezium is 180 cm² .

Height is 9 cm

one of the parallel sides is longer than the other by 6 cm

Required to find :-

• Measurements of the two parallel sides ?

Formula used :-

$\large{\leadsto{\boxed{\rm{ Area \; of \; a \; Trapezium = \dfrac{1}{2}\times h( a + b )}}}}$

Solution :-

Given that :-

The area of the Trapezium is 180 cm²

Height is 9 cm

one of the parallel sides is longer than the other by 6 cm

And

He asked us to find the measurements of the two sides .

So,

Using the formula ,

$\large{\leadsto{\boxed{\rm{ Area \; of \; a \; Trapezium = \dfrac{1}{2}\times h( a + b )}}}}$

Here,

h = height or distance between the parallel sides

a , b = measurements of the two parallel sides

So,

Let,

The longest side of the Trapezium be as " a "

So,

It is given that the one of side is longer than the other side by 6 cm .

Hence,

Let the side a be as x + 6 cm

Similarly,

The side b as x cm

Now substitute these values in the above formula .

So,

$\longrightarrow{\tt{ Area = \dfrac{1}{2} \times 9 ( x + 6 + x ) }}$

$\longrightarrow{\rm{ 180 = \dfrac{1}{2} \times 9 ( 2x + 6 ) }}$

$\longrightarrow{\tt{ 180 \times 2 = 9 ( 2x + 6 ) }}$

$\longrightarrow{\rm{ 360 = 9 ( 2x + 6 ) }}$

$\longrightarrow{\tt{ 360 = 18x + 54 }}$

$\longrightarrow{\rm{ 18x + 54 = 360 }}$

$\longrightarrow{\tt{ 18x = 360 - 54 }}$

$\longrightarrow{\rm{ 18x = 306 }}$

$\implies{\tt{ x = \dfrac{306}{18}}}$

$\implies{\rm{ x = 17 \; cm }}$

So,

value of X is 17 cm .

Now substitute this value in a & b .

Hence,

a = x + 6

➜ 17 + 6 = 23 cm

b = x

➜ 17 cm

Therefore,

Measurements of the two parallel sides are 23 cm & 17 cm

Points to remember :-

1. Formula :-

$\large{\leadsto{\boxed{\rm{ Area \; of \; a \; Trapezium = \dfrac{1}{2}\times h( a + b )}}}}$

2. Properties of trapezium are ,

• One pair of opposite sides are parallel .

• Sum of two adjacent angles is supplementary .

• Diagonals bisect each other

• Sum of all angles is equal to 360°

3. If the non - parallel sides are equal then the trapezium is also known as Isosceles Trapezium .

4. The distance between the parallel sides is also known as the height of the Trapezium . It is denoted by " h " .