Area and Perimeter
 Area of a square is 1/2 hectare. The diagonal of the square is?

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Area = 1/2 hectare = 10000 / 2 m^{2}
= 5000 m^{2}
Again Area = 1/2 x (Diagonal)^{2}Correct Option: B
Area = 1/2 hectare = 10000 / 2 m^{2}
= 5000 m^{2}
Again Area = 1/2 x (Diagonal)^{2}
So 1/2 x (Diagonal)^{2} = 5000m^{2}
⇒ Diagonal^{2}= 10000
∴ Diagonal = 100
 The base of rightangled triangle is 5 meters and hypotenuse is 13 meters . Its area will be ?

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Altitude = √(13)^{2}  (5)^{2}
= √144 = 12mCorrect Option: C
Altitude = √(13)^{2}  (5)^{2}
= √144 = 12m
∴ Area of the triangle = (5 x 12 ) / 2 m^{2}
= 30m^{2}
 The length of a rectangle is double while its breadth is halved. What is the percentage change in area ?

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Let length = l and breadth = b
Then, area = lb
New length = 2l
and new breadth = b/2
∴ New area = ( 2l ) x (b/2) = lbCorrect Option: C
Let length = l and breadth = b
Then, area = lb
New length = 2l
And new breadth = b/2
∴ New area = ( 2l ) x (b/2) = lb
So, there is no change in area .
 The cost of carpeting a room 15 meters long with a carpet 75 cm wide at 30 paisa per meter is Rs. 36. The breadth of the room is ?

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Length of carpet = Total Cost / Rate
= 3600 / 30
= 120 m
Area of carpet = (120 x 75) / 100 m^{2}
= 90 m^{2}
∴ Area of the room = 90 m^{2}Correct Option: A
Length of carpet = Total Cost / Rate
= 3600 / 30
= 120 m
Area of carpet = (120 x 75) / 100 m^{2}
= 90 m^{2}
∴ Area of the room = 90 m^{2}
Breadth of the room = Area /Length
= 90 / 15 m
= 6m
 If the side of a square is increased by 25%, then how much percent does its area get increased ?

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Let area 100 m^{2}
Then, side = 10 m
New side = 125 % of 10
= (125/100) x 10)
= 12.5 m
New area = 12.5 x 12.5 m^{2}
=(12.5)^{2} sq. mCorrect Option: D
Let area 100 m^{2}
Then, side = 10 m
New side = 125 % of 10
= (125/100) x 10
= 12.5 m
New area = 12.5 x 12.5 m^{2}
=(12.5)^{2} sq. m
∴ Increase in area = (12.5)^{2}  (10)^{2} m^{2}
= 22.5 x 2.5 m^{2}
=56.25 m^{2}
% Increase = 56.25 %