Area of Trapezium Class 8, deals with various types of questions which are as under:-

- Area of Trapezium
- Finding Length of one of Parallel sides of Trapezium
- Find Parallel sides of Trapezium when their difference given
- Finding parallel sides of Trapezium

#### Area of Trapezium Class 8 – Area of Trapezium

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

**Question 1**

In a trapezium, the parallel sides are 4 cm and 5 cm, and the distance between them is 6 cm, find its area?

**Explanation:**

Given:

Length of one of the parallel side = 4 cm

Length of other parallel side = 5 cm

Distance between parallel sides = 6 cm

Area of trapezium = 1/2 x ( sum of two parallel sides ) x ( distance between them )

= { 1/2 x ( 4 + 5 ) x 6 } cm²

= { 1/2 x ( 9 ) x 6 } cm²

= 54/2 cm²

= 27 cm²

#### Area of Trapezium Class 8 – Finding Length of one of Parallel sides of Trapezium

**Question 2**

The area of trapezium is 27 cm² and the distance between its parallel sides is 6 cm . If the length of its one of the parallel side is 3 cm , find the length of the other parallel side?

**Explanation:**

Given:

Area of trapezium = 27 cm²

Distance between parallel sides = 6 cm

Length of one of the parallel side = 3 cm

Length of other parallel side = ?

Let the length of the other parallel side be y cm

Area of trapezium = 1/2 x ( sum of two parallel sides ) x ( distance between them )

27 cm² = { 1/2 x ( 3 + y ) x 6 } cm²

27 = 9 + 3y

27 – 9 = 3y

3y = 18

y = 18/3

y = 6

Hence, the length of other parallel side is 6 cm

#### Area of Trapezium Class 8 – Find Parallel sides of Trapezium when their difference given

**Question 3**

The area of trapezium is 30 cm² and the distance between its parallel sides is 6 cm. If difference between the length of parallel sides is 2 cm, find the length of its parallel sides ?

**Explanation:**

Given:

Area of trapezium = 30 cm²

Distance between parallel sides = 6 cm

Difference between the length of parallel sides = 2 cm

Let the length of one parallel side be y cm

then, the length of other parallel side be ( y + 2 ) cm

Area of trapezium = 1/2 x ( sum of two parallel sides ) x ( distance between them )

30 cm² = { 1/2 x ( y + y + 2 ) x 6 } cm²

30 = { 1/2 x ( 2y + 2 ) x 6 }

30 = { ( 2y + 2 ) x 3

30/3 = 2y + 2

10 = 2y + 2

10 – 2 = 2y

8 = 2y

y = 8/2

y = 4

Therefore,

Length of one of its parallel side = y cm = 4 cm

Length of other parallel side = ( y + 2 ) cm = ( 4 + 2 ) cm = 6 cm

#### Area of Trapezium Class 8 – Finding parallel sides of Trapezium

**Question 4**

The area of trapezium is 36 cm² and the perpendicular distance between the parallel sides is 8 cm. If the ratio of its parallel sides are 1 : 2, then find its smaller side ?

**Explanation:**

Given:

Area of trapezium = 36 cm²

Distance between parallel sides = 8 cm

Ratio of its parallel sides = 1 : 2

Let the length of one parallel side be 1y cm

then, the length of other parallel side would be 2y cm

Area of trapezium = 1/2 x ( sum of two parallel sides ) x ( distance between them )

36 cm² = { 1/2 x ( 1y + 2y ) x 8 } cm²

36 = { 1/2 x ( 3y ) x 8 }

36 = ( 3y x 4 )

36/(4 x 3) = y

y = 3

Therefore,

Length of one of its parallel side = 1y cm = ( 1 x 3 ) cm = 3 cm

Length of its other parallel side = 2y cm = ( 2 x 3 ) cm = 6 cm

Hence, the length of the smaller side is 3 cm

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