The area of a trapezium shaped field is 480m, the distance between two parallel sides is 5m and one of the parallel side is 20m. find the other parallel side.
Answers
Let ABCD be a trapezium with parallel sides AB and CD
Let AB=20 ...(Given) and CD=x
A(□ABCD)=480 m
2
,height(h)=15 m ... (Given)
We know that, A(□ABCD)=
2
(AB+CD)
×h
⟹480=
2
20+x
×15
⟹
15
2×480
=20+x
⟹64=20+x
⟹x=44
Hence, length of other parallel side CD is 44 m
Given :
- Area of Trapezium = 480m²
- Height of Trapezium= 5m²
- One Parallel Side = 20m
To Find :
- Second Parallel Side
Solution :
✰ As we know that, Area of Trapezium is given by ½ × Height × (Sum of Two Parallel Sides).
✰ Now, In this question Area of Trapezium , Height of Trapezium , One parallel side of Trapezium are given . So Let's Assume the Second Parallel Side be x . Now, we will simply fill the given values in the Formula to find the Second Parallel Side.
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⟹ Area of Trapezium = ½ × H × (S1 + S2)
⟹ 480 = ½ × 5 × (20 + x)
⟹ 480 × 2 = 5 × (20 + x)
⟹ 960 = 5 × (20 + x)
⟹ 960 / 5 = 20 + x
⟹ 192 = 20 + x
⟹ 192 - 20 = x
⟹ 172 = x
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Verification :
➟ Area = ½ × H × (S1 + S2)
➟ Area = ½ × 5 × (20 + 172)
➟ Area = ½ × 5 × 192
➟ Area = 5 × 96
➟ 480 = 480
Hence Verified
Thus Second Parallel Side is 172m
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