if area of a parallelogram with sides a and b is A and that of rectangle with sides a and b is B then a) A greater than B , A equal to B , A lesser than B ,
Answers
A is lesser than B.
Step-by-step explanation:
Area of parallelogram of sides a and b = A = b * h where h is the height.
Height can be solved using Pythagoras theorem. But h is generally a smaller value than a, as a will be the hypotenuse.
Area of rectangle of sides a and b = B = a * b
So b* h will be smaller than b * a
Area of parallelogram will be lesser than area of the rectangle.
Therefore A is lesser than B.
Given : area of a parallelogram with sides a and b is A and that of rectangle with sides a and b is B
To find : Choose correct option
A greater than B , A equal to B , A lesser than B ,
Solution:
Area of Parallelogram A = absinθ
Area of rectangle B = ab
0<θ<π
0<sinθ≤1
absinθ = ab
when sinθ = 1
Means θ = π/2 hence rectangle
for all other θ
0 < sinθ < 1
Hence absinθ < ab
=> A < B
A lesser than B
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