The area of a trapezium is 180cm square and it's height is 9cm.If one

1.	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» 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 " .

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»

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 " .