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