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Area and Perimeter

  1. Area of a square is 1/2 hectare. The diagonal of the square is?
    1. 250 meter
    2. 100 meter
    3. 50√ 2 meter
    4. 50 meter
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    Area = 1/2 hectare = 10000 / 2 m2
    = 5000 m2

    Again Area = 1/2 x (Diagonal)2

    Correct Option: B

    Area = 1/2 hectare = 10000 / 2 m2
    = 5000 m2

    Again Area = 1/2 x (Diagonal)2

    So 1/2 x (Diagonal)2 = 5000m2
    ⇒ Diagonal2= 10000
    ∴ Diagonal = 100

    Report

  1. The base of right-angled triangle is 5 meters and hypotenuse is 13 meters . Its area will be ?
    1. 25m2
    2. 28 m2
    3. 30m2
    4. None of these
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    Altitude = √(13)2 - (5)2
    = √144 = 12m

    Correct Option: C

    Altitude = √(13)2 - (5)2
    = √144 = 12m

    ∴ Area of the triangle = (5 x 12 ) / 2 m2
    = 30m2

    Report

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  1. The length of a rectangle is double while its breadth is halved. What is the percentage change in area ?
    1. 50
    2. 75
    3. No change
    4. None of these
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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) = lb

    Correct 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 .

    Report

  1. 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 ?
    1. 6 meters
    2. 8 meters
    3. 9 meters
    4. 12 meters
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    Length of carpet = Total Cost / Rate
    = 3600 / 30
    = 120 m

    Area of carpet = (120 x 75) / 100 m2
    = 90 m2
    ∴ Area of the room = 90 m2

    Correct Option: A

    Length of carpet = Total Cost / Rate
    = 3600 / 30
    = 120 m

    Area of carpet = (120 x 75) / 100 m2
    = 90 m2
    ∴ Area of the room = 90 m2

    Breadth of the room = Area /Length
    = 90 / 15 m
    = 6m

    Report

  1. If the side of a square is increased by 25%, then how much percent does its area get increased ?
    1. 125
    2. 156.25
    3. 50
    4. 56.25
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    Let area 100 m2
    Then, side = 10 m

    New side = 125 % of 10
    = (125/100) x 10)
    = 12.5 m

    New area = 12.5 x 12.5 m2
    =(12.5)2 sq. m

    Correct Option: D

    Let area 100 m2
    Then, side = 10 m

    New side = 125 % of 10
    = (125/100) x 10
    = 12.5 m

    New area = 12.5 x 12.5 m2
    =(12.5)2 sq. m

    ∴ Increase in area = (12.5)2 - (10)2 m2
    = 22.5 x 2.5 m2
    =56.25 m2

    % Increase = 56.25 %

    Report

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