Area and Perimeter


  1. Find the cost of carpeting a room 8 m long and 6 m broad with a carpet 75 cm wide at ₹ 20 per m.











  1. View Hint View Answer Discuss in Forum

    Area of the carpet = Area of the room

    Correct Option: D

    Area of the carpet = Area of the room
    = 8 x 6 = 48 sq m

    Width of the carpet = 75/100 = 3/4 m

    Length of the carpet = 48 x (4/3)
    = 16 x 4 = 64 m

    ∴ Cost of carpeting = 64 x 20 = ₹ 1280


  1. A rectangle has 20 cm as its length and 200 sq cm as its area. If the area is increased by 11/5 time the original area by increase its length only then the perimeter of the rectangle so formed (in cm) is









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    l1 = 20 cm, A1 = 200 sq cm
    ∴ b1 = 200/20 = 10 cm
    Now, A2 = 200 x 6/5 = 240 sq cm
    b2 = 10 cm
    ∴ l2 = 240/10 = 24 cm

    ∴ Perimeter of new rectangle = 2(l2 + b2)

    Correct Option: D

    l1 = 20 cm, A1 = 200 sq cm
    ∴ b1 = 200/20 = 10 cm
    Now, A2 = 200 x 6/5 = 240 sq cm
    b2 = 10 cm
    ∴ l2 = 240/10 = 24 cm

    ∴ Perimeter of new rectangle = 2(l2 + b2)
    = 2(24 + 10) = 2 x 34 = 68 cm



  1. The breadth of a rectangle is 25 m. The total cost of putting a grass bed on this field was ₹ 12375, at the rate of ₹ 15 per sq m. What is the length of the rectangular field?











  1. View Hint View Answer Discuss in Forum

    Area to the rectangular field = 12375/15 = 825 sq m
    According to the question,
    (L x B) = 825 [L = length and B = breadth]

    Correct Option: C

    Area to the rectangular field = 12375/15 = 825 sq m
    According to the question,
    (L x B) = 825 [L = length and B = breadth]
    ⇒ L x 25 = 825
    ∴ L = 825/25 = 33 m


  1. What is the area of a square having perimeter 68 cm?











  1. View Hint View Answer Discuss in Forum

    According to the question,
    4a = 68 [ where a = side]
    ∴a = 68/4 = 17 cm
    ∴ Required area = a2

    Correct Option: C

    According to the question,
    4a = 68 [ where a = side]
    ∴a = 68/4 = 17 cm

    ∴ Required area = a2
    = (17)2 = 289 sq cm



  1. A railing of 288 m is required for fencing a semi-circular park. Find the area of the park. (π = 22/7)









  1. View Hint View Answer Discuss in Forum

    Let the radius of the park be r, then
    πr + 2r = 288

    Area of the park = (1/2)πr2

    Correct Option: A

    Let the radius of the park be r, then
    πr + 2r = 288
    (π + 2)r = 288
    ⇒ [(22/7) + 2]r = 288
    ⇒ r = (288 x 7)/36 = 56

    ∴ Area of the park = (1/2)πr2
    = (1/2) x (22/7) x 56 x 56
    = 4928