10. The area of a trapezium is 84 sq. m and the distance between its parallel sides are 6 m. If the length of one of the parallel sides is 5 m, then the length of the other is:
a. 30 cm
b. 30 m
c. 28 m
d. 23 m
Answers
Answer :
The other parallel side of the trapezium = 23 m
Option (d) → 23 m
Given :
- Area of trapezium = 84 m²
- Distance between it's parallel sides = 6 m
- Length of one parallel side = 5 m
To find :
- Length of the other parallel side
Solution :
Here, we are given the area, distance between the parallel sides and the length of one of the parallel side of the trapezium and we need to calculate the length of the other parallel side. So, to calculate it we will use the formula of area of trapezium.
Formula of area of trapezium :
- Area of trapezium = ½ × Sum of the parallel sides × Distance between them
we have,
- Area = 84 m²
- Sum of parallel sides = ?
- Distance between them = 6 m
Neither we have the value of sum of parallel sides of the trapezium nor we have one of the parallel side of the trapezium. So, we will assume the other parallel side of the trapezium as any variable.
Let,
- The other parallel side of the trapezium = x metre
→ Sum of the parallel sides of the trapezium = (5 + x) metre
Now, applying the values in the formula of area of trapezium :
→ 84 = ½ × (5 + x) × 6
→ 84 = (5 + x) × 3
→ 84/3 = 5 + x
→ 28 = 5 + x
→ 28 - 5 = x
→ 23 = x
Therefore, the other parallel side of the trapezium = x = 23 m