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 = 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 = x ( sum of two parallel sides ) x ( distance between them )

= { x ( 4 + 5 ) x 6 }

= { x ( 9 ) x 6 }

=

= 27

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

**Question 2**

The area of trapezium is 27 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 =

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 = x ( sum of two parallel sides ) x ( distance between them )

27 = { x ( 3 + y ) x 6 }

27 = 9 + 3y

27 – 9 = 3y

3y = 18

y =

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 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

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 = x ( sum of two parallel sides ) x ( distance between them )

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

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

30 = { ( 2y + 2 ) x 3

= 2y + 2

10 = 2y + 2

10 – 2 = 2y

8 = 2y

y =

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 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

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 = x ( sum of two parallel sides ) x ( distance between them )

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

36 = { x ( 3y ) x 8 }

36 = ( 3y x 4 )

= 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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