Find the two parallel sides of a trapezium whose area is 1.6 m², altitude is 10 dm and
one of the parallel sides is longer than the other by 8 dm.
Answers
Answer:
Step-by-step explanation:
Given :-
Area of trapezium = 1.6 sq m
Altitude, h = 10 dm = 1 m
To Find :-
The two parallel sides.
Formula to be used :-
Area of trapezium
Solution :-
Let one of the parallel sides be x
And the other side be (x + 0.8) m
According to the Question
Area of trapezium, A = (1/2) × h × (a + b)
⇒ 1.6 = (1/2) × 1 × (x + x + 0.8)
⇒ 3.2 = 2x + 0.8
⇒ 2x = 3.2 - 0.8 = 2.4
⇒ x = 1.2 m
1st Side = 1.2 m
2nd Side = (x + 0.8) = 2 m
Hence, the parallel sides are 1.2 m and 2 m.
• Let one parallel side of trapezium be (M) m.
» One of the parallel sides is longer than the other by 8 m.
• Another side of trapezium be (M + 0.8) m.
• Area of trapezium = 1.6 m²
__________ [ GIVEN ]
• We have to find the two parallel sides of the trapezium.
____________________________
We know that..
» Area of trapezium = 1/2 × h × (d1 + d2)
Here..
d1 = M
d2 = M + 0.8
Put the known values in above formula
→ 1.6 = 1/2 × 1 × (M + M + 0.8)
→ 1.6 = 1/2 (2M + 0.8)
→ 1.6 = 1/2 × 2(M + 0.4)
→ 1.6 = M + 0.4
→ 1.6 - 0.4 = M
→ 1.2 = M
→ M = 1.2
____________________________
• One parallel side of trapezium = M
→ 1.2 m
• Another parallel side of trapezium = M + 0.8
→ 1.2 + 0.8
→ 2 m
___________________________
1.2 m and 2 m is the are the two parallel sides of the trapezium.
_______ [ ANSWER ]
___________________________