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Answers
Answer:The height of the parallelogram will be 6cm.
Step-by-step explanation:
1. Find the area of triangle using Herons formula. It will come out to be 84
2. The area of parallelogram will also be 84. So base.height =84.
3. Since base is given as 14cm so height = 84/14= 6cm.
Step-by-step explanation:
Given :-
A triangle and a Parallelogram have the same base and the same area .The sides of a triangle are 13 cm , 14 cm and 15 cm and the paralellogram stands on the base 14 cm
To find :-
Find the height of the Parallelogram ?
Solution :-
Given that
A triangle and a Parallelogram have the same base and the same area .
=> Area of the triangle = Area of a Parallelogram
Finding area of. the triangle :-
The sides of a triangle are 13 cm ,14 cm and 15 cm
Let a = 13 cm
Let b = 14 cm
Let c = 15 cm
We know that
By Heron's formula
Area of a triangle =√[S(S-a)(S-b)(S-c)] sq.units
Where , S = (a+b+c)/2 units
S = (13+14+15)/2 cm
=> S = 42/2 cm
=> S = 21 cm
Area = √[21(21-13)(21-14)(21-15)]
=> Area = √(21×8×7×6)
=> Area = √(3×7×7×2×2×2×2×3)
=> Area = √[(2×2)×3×3)×(2×2)×(7×7)]
=> Area = 2×2×3×7
=> Area = 84 sq.cm
Area of the given triangle = 84 cm² -------(1)
Finding Area of the paralellogram:-
Given that the paralellogram stands on the base 14 cm
Base of the paralellogram = 14 cm
Let the height of the Parallelogram be h cm
We know that
Area of a Parallelogram = bh sq.units
Area of the given Parallelogram = 14×h cm²
Area of the Parallelogram = 14h cm²------(2)
Given that
Both areas are equal
=> (1) = (2)
=> 14h = 84
=> h = 84/14
=> h = 6 cm
Therefore,height = 6 cm
Answer:-
The height of the given Parallelogram for the given problem is 6 cm
Used formulae:-
Heron's formula :-
- Area of a triangle =√[S(S-a)(S-b)(S-c)] sq.units
- S = (a+b+c)/2 units
- Area of a Parallelogram = bh sq.units
