1. Find the area (in square metres) of a rectangle whose
    (i) length = 6.2 m, breadth = 2.3 m
    (ii) length = 210 cm, breadth = 145 cm
  2. Find the area (in square centimetres) of a square whose side is
    (i) 3.1 cm
    (ii) 1.5 dm
  3. Find the area (in square metres) of a square whose side is 12.4 dam.
  4. Find the area of a rectangular field in acres whose sides are:
    (i) 250 m and 160 m
    (ii) 80 m 3 dm and 140 m
  5. A wall measures 9.5 m by 8.5 m. There is a door on it measuring 2.2 m by 1.8 m. If painting costs Rs 3.25 per m², find the cost of painting the wall (excluding the door).
  6. A wire is bent into a rectangle of size 44 cm by 28 cm. The same wire is then re-bent to form a square.
    (a) Find the side of that square.
    (b) Which shape (the original rectangle or the square) encloses more area? Give the areas.
  7. How many square metres of glass are needed for a window that has 15 panes, each measuring 30 cm by 18 cm?
  8. A tile measures 12 cm by 15 cm. How many such tiles are required to cover a wall of size 2.8 m by 3.6 m? Also find the total cost if each tile costs Rs 3.
  9. A room measures 8.4 m by 5.6 m. It is to be paved with rectangular tiles each 25 cm by 12 cm. Find total number of tiles required and the total cost if each tile costs Rs 2.75.
  10. One side of a square field is 185 m. Find the cost of turfing the field at the rate of Rs 1.80 per m².
  11. A rectangular field is 320 m by 210 m. How long will it take a girl to go twice around the field if she walks at 1.75 m/s?
  12. A corridor is 9 m long and 7 m wide. Canvas sheets measuring 2 m by 1 m are used to cover it. If each sheet costs Rs 9, find the cost to cover the corridor (use whole sheets only).
  13. A playground is 70 m 45 cm by 30 m 25 cm.
    (i) Find the cost of turfing it at Rs 3 per m².
    (ii) How long will a man take to walk three times around it at 2 m/s?
  14. A lane 200 m long and 6 m wide is to be paved with bricks each 20 cm by 10 cm. Bricks cost Rs 820 per thousand. Find the number of bricks required and the total cost.
  15. From a sheet of paper 132 cm by 92 cm, how many envelopes of size 16 cm by 8 cm can be cut (assume all envelopes are cut without waste by arranging them in rows and columns)?
  16. The width of a cloth roll is 150 cm. How many metres of cloth are required to make 25 diapers if each diaper needs a piece 45 cm by 30 cm? (Assume the 30 cm side is taken across the width of the cloth.)
  17. A room 6.2 m by 5.4 m is carpeted at a total cost of Rs 3840. The carpet roll is 80 cm wide. Find the cost of the carpet per metre (i.e., cost per running metre of the roll).
  18. A room is 8.5 m long, 7.2 m broad and 3.6 m high. It has one door 2.2 m × 1.5 m and two windows of sizes 1.2 m × 1.5 m and 1.5 m × 1.2 m. Find the cost of whitewashing the walls at Rs 4.50 per m² (exclude floor and ceiling; exclude door and windows area).
  19. A hall is 40 m long and 28 m broad. Allow 96 m² for doors and windows. If papering the walls costs Rs 9 per m² and the total papering cost is Rs 9,408, find the height of the hall.
  20. A rectangular swimming pool is 25 m long and 12 m wide. It is surrounded by a 1.5 m wide path. Find the area of the path and the cost of cementing it at the rate of Rs 85 per m².

 

 

 

 

ANSWER KEY

1. (i) Area = 6.2 × 2.3 = 14.26 m².
(ii) Convert to metres: 210 cm = 2.10 m, 145 cm = 1.45 m. Area = 2.10 × 1.45 = 3.045 m².

2. (i) Side = 3.1 cm ⇒ Area = (3.1)² = 9.61 cm².
(ii) 1.5 dm = 15 cm ⇒ Area = 15 × 15 = 225 cm².

3. 1 dam = 10 m. Side = 12.4 dam = 124 m. Area = 124² = 15,376 m².

4. (i) Area = 250 × 160 = 40,000 m². 1 acre ≈ 4,046.8564224 m².
Area in acres = 40,000 ÷ 4,046.8564224 ≈ 9.884 acres (approx).

(ii) 80 m 3 dm = 80.3 m. Area = 80.3 × 140 = 11,242 m².
In acres = 11,242 ÷ 4,046.8564224 ≈ 2.778 acres (approx).

5. Wall area = 9.5 × 8.5 = 80.75 m². Door area = 2.2 × 1.8 = 3.96 m².
Net area = 80.75 − 3.96 = 76.79 m². Cost = 76.79 × 3.25 = Rs 249.57 (≈ Rs 249.57).

6. Rectangle perimeter = 2(44 + 28) = 2 × 72 = 144 cm. Re-bent as square ⇒ side = 144 ÷ 4 = 36 cm.
Area of rectangle = 44 × 28 = 1,232 cm². Area of square = 36² = 1,296 cm².
Square encloses more area (1,296 cm² > 1,232 cm²).

7. Each pane area = 30 cm × 18 cm = 540 cm² = 0.054 m². For 15 panes: total = 15 × 0.054 = 0.81 m².

8. Tile = 12 cm × 15 cm = 0.12 × 0.15 = 0.018 m². Wall area = 2.8 × 3.6 = 10.08 m².
Number of tiles = 10.08 ÷ 0.018 = 560 tiles exactly. Cost = 560 × 3 = Rs 1,680.

9. Room area = 8.4 × 5.6 = 47.04 m². Tile area = 0.25 × 0.12 = 0.03 m².
Number of tiles = 47.04 ÷ 0.03 = 1,568 → whole tiles ⇒ 1,568 tiles.
Cost = 1,568 × 2.75 = Rs 4,312.00.

10. Area = 185² = 34,225 m². Cost = 34,225 × 1.80 = Rs 61,605.00.

11. Perimeter = 2(320 + 210) = 2 × 530 = 1,060 m. Twice around = 2 × 1,060 = 2,120 m.
Time = distance ÷ speed = 2,120 ÷ 1.75 ≈ 1,211.43 s (≈ 20 min 11.43 s).

12. Corridor area = 9 × 7 = 63 m². Each sheet = 2 × 1 = 2 m². Sheets needed = 63 ÷ 2 = 31.5 ⇒ whole sheets ⇒ 32 sheets.
Cost = 32 × 9 = Rs 288.

13. Length = 70 + 0.45 = 70.45 m. Breadth = 30 + 0.25 = 30.25 m. Area = 70.45 × 30.25 = 2,131.1125 m².
Cost at Rs 3/m² = 2,131.1125 × 3 = Rs 6,393.34 (approx).
Perimeter = 2(70.45 + 30.25) = 2 × 100.7 = 201.4 m. Three rounds = 3 × 201.4 = 604.2 m. Time at 2 m/s = 604.2 ÷ 2 = 302.1 s (≈ 5 min 2.1 s).

14. Lane area = 200 × 6 = 1,200 m². Brick area = 0.20 × 0.10 = 0.02 m². Bricks needed = 1,200 ÷ 0.02 = 60,000 bricks.
Cost = (60,000 ÷ 1,000) × 820 = 60 × 820 = Rs 49,200.

15. Fit envelopes in rows and columns: along length 132 cm ÷ 16 cm = 8 (whole), along breadth 92 ÷ 8 = 11 (whole). Total = 8 × 11 = 88 envelopes.

16. Cloth width = 150 cm. Each diaper piece = 45 cm × 30 cm; assume 30 cm is across width. Number across width = floor(150 ÷ 30) = 5 diapers per length-row. For 25 diapers you need ceil(25 ÷ 5) = 5 rows. Each row uses 45 cm (0.45 m) of length. Total length = 5 × 0.45 = 2.25 m.

17. Room area = 6.2 × 5.4 = 33.48 m². Roll width = 0.8 m. Length of roll used = 33.48 ÷ 0.8 = 41.85 m. Cost per metre = 3,840 ÷ 41.85 ≈ Rs 91.76 per m.

18. Perimeter = 2(8.5 + 7.2) = 2 × 15.7 = 31.4 m. Wall area = perimeter × height = 31.4 × 3.6 = 113.04 m².
Openings area = door 2.2×1.5 = 3.30 m²; windows = 1.2×1.5 = 1.80 m² and 1.5×1.2 = 1.80 m² ⇒ total openings = 3.30 + 1.80 + 1.80 = 6.90 m².
Net area = 113.04 − 6.90 = 106.14 m². Cost = 106.14 × 4.50 = Rs 477.63 (approx).

19. Let height = h. Perimeter = 2(40 + 28) = 136 m. Area to paper = (perimeter × h) − 96. Cost = 9 × [(136h) − 96] = 9,408.
So (136h − 96) = 9,408 ÷ 9 = 1,045.333… ⇒ 136h = 1,045.333… + 96 = 1,141.333… ⇒ h = 1,141.333… ÷ 136 ≈ 8.392 m.

20. Area of path = 120 m², Cost = Rs 10,200

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