Perimeter & Area

65 Class 6 IMO Mathematics Olympiad practice questions on perimeter & area, part of the Geometry & Spatial Thinking topic area. Every question below includes the correct answer and a full explanation.

1. 1. What is the perimeter of a square with side 9 cm?

   • A.18
   • B.27
   • C.36
   • D.81
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   Answer: C. 36

   4 × 9 = 36 cm.

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2. 2. What is the area of a rectangle with length 8 cm and breadth 5 cm?

   • A.13
   • B.26
   • C.40
   • D.45
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   Answer: C. 40

   8 × 5 = 40 cm².

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3. 3. A square has side 15 cm. What is its perimeter?

   • A.225
   • B.64
   • C.60
   • D.45
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   Answer: C. 60

   4 × 15 = 60 cm.

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4. 4. A square has side 18 cm. What is its perimeter?

   • A.54
   • B.76
   • C.324
   • D.72
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   Answer: D. 72

   4 × 18 = 72 cm.

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5. 5. A rectangle is 13 cm long and 8 cm wide. What is its area?

   • A.114
   • B.42
   • C.104
   • D.21
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   Answer: C. 104

   13 × 8 = 104 cm².

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6. 6. A rectangle is 12 cm long and 9 cm wide. What is its area?

   • A.118
   • B.108
   • C.42
   • D.21
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   Answer: B. 108

   12 × 9 = 108 cm².

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7. 7. A rectangle is 13 cm long and 11 cm wide. What is its area?

   • A.143
   • B.48
   • C.153
   • D.24
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   Answer: A. 143

   13 × 11 = 143 cm².

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8. 8. A rectangle is 11 cm long and 5 cm wide. What is its area?

   • A.55
   • B.16
   • C.65
   • D.32
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   Answer: A. 55

   11 × 5 = 55 cm².

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9. 9. A rectangle is 19 m long and 13 m wide. What is its perimeter?

   • A.45
   • B.51
   • C.247
   • D.64
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   Answer: D. 64

   2 × (19 + 13) = 64 m.

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10. 10. A rectangle is 29 m long and 15 m wide. What is its perimeter?

    • A.59
    • B.73
    • C.88
    • D.435
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    Answer: C. 88

    2 × (29 + 15) = 88 m.

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11. 11. What is the area of a square with side 13 cm?

    • A.52
    • B.26
    • C.173
    • D.169
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    Answer: D. 169

    13 × 13 = 169 cm².

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12. 12. What is the area of a square with side 7 cm?

    • A.53
    • B.14
    • C.49
    • D.28
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    Answer: C. 49

    7 × 7 = 49 cm².

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13. 13. What is the area of a square with side 9 cm?

    • A.81
    • B.85
    • C.36
    • D.18
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    Answer: A. 81

    9 × 9 = 81 cm².

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14. 14. A rectangle is 18 m long and 8 m wide. What is its perimeter?

    • A.44
    • B.144
    • C.52
    • D.34
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    Answer: C. 52

    2 × (18 + 8) = 52 m.

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15. 15. What is the area of a rectangle measuring 16 cm by 6 cm?

    • A.106
    • B.96
    • C.44
    • D.22
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    Answer: B. 96

    16 × 6 = 96 cm².

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16. 16. A square has area 49 cm². What is the length of its side?

    • A.6
    • B.7
    • C.8
    • D.9
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    Answer: B. 7

    √49 = 7.

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17. 17. What is the perimeter of a rectangle with length 15 m and breadth 9 m?

    • A.24
    • B.42
    • C.48
    • D.54
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    Answer: C. 48

    2 × (15 + 9) = 2 × 24 = 48 m.

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18. 18. A square has perimeter 32 cm. What is its area?

    • A.16
    • B.32
    • C.64
    • D.128
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    Answer: C. 64

    Side = 32 ÷ 4 = 8 cm, so area = 8 × 8 = 64 cm².

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19. 19. What is the area of a square with side 11 cm?

    • A.44
    • B.110
    • C.121
    • D.132
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    Answer: C. 121

    11 × 11 = 121 cm².

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20. 20. What is the perimeter of a rectangle with length 22 cm and breadth 14 cm?

    • A.36
    • B.58
    • C.72
    • D.88
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    Answer: C. 72

    2 × (22 + 14) = 2 × 36 = 72 cm.

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21. 21. A rectangle has area 48 cm² and breadth 6 cm. What is its length?

    • A.6
    • B.7
    • C.8
    • D.9
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    Answer: C. 8

    48 ÷ 6 = 8 cm.

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22. 22. A rectangle is 14 cm long and 9 cm wide. Its perimeter is:

    • A.23 cm
    • B.36 cm
    • C.46 cm
    • D.126 cm
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    Answer: C. 46 cm

    2 × (14+9) = 46 cm.

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23. 23. The area of a square is 81 cm². Its perimeter is:

    • A.18 cm
    • B.27 cm
    • C.36 cm
    • D.40 cm
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    Answer: C. 36 cm

    Side = √81 = 9 cm. Perimeter = 4×9 = 36 cm.

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24. 24. A rectangular playground is 30 m long and 18 m wide. What is the distance around it?

    • A.48 m
    • B.78 m
    • C.96 m
    • D.108 m
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    Answer: C. 96 m

    2 × (30+18) = 96 m.

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25. 25. A rectangle is 12 cm long and 11 cm wide. What is its area?

    • A.46
    • B.23
    • C.132
    • D.142
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    Answer: C. 132

    12 × 11 = 132 cm².

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26. 26. A square has side 5 cm. What is its perimeter?

    • A.15
    • B.24
    • C.20
    • D.25
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    Answer: C. 20

    4 × 5 = 20 cm.

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27. 27. A rectangle is 9 cm long and 8 cm wide. What is its area?

    • A.82
    • B.34
    • C.72
    • D.17
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    Answer: C. 72

    9 × 8 = 72 cm².

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28. 28. A rectangle is 15 cm long and 11 cm wide. What is its area?

    • A.52
    • B.165
    • C.175
    • D.26
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    Answer: B. 165

    15 × 11 = 165 cm².

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29. 29. A square has side 7 cm. What is its perimeter?

    • A.28
    • B.49
    • C.21
    • D.32
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    Answer: A. 28

    4 × 7 = 28 cm.

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30. 30. What is the area of a square with side 5 cm?

    • A.25
    • B.20
    • C.29
    • D.10
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    Answer: A. 25

    5 × 5 = 25 cm².

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31. 31. What is the area of a rectangle measuring 9 cm by 11 cm?

    • A.40
    • B.20
    • C.99
    • D.109
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    Answer: C. 99

    9 × 11 = 99 cm².

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32. 32. What is the area of a square with side 10 cm?

    • A.100
    • B.40
    • C.20
    • D.104
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    Answer: A. 100

    10 × 10 = 100 cm².

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33. 33. What is the area of a rectangle measuring 23 cm by 7 cm?

    • A.161
    • B.60
    • C.171
    • D.30
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    Answer: A. 161

    23 × 7 = 161 cm².

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34. 34. What is the area of a rectangle measuring 8 cm by 12 cm?

    • A.96
    • B.40
    • C.20
    • D.106
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    Answer: A. 96

    8 × 12 = 96 cm².

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35. 35. What is the area of a square with side 12 cm?

    • A.144
    • B.148
    • C.48
    • D.24
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    Answer: A. 144

    12 × 12 = 144 cm².

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36. 36. A rectangle is 27 m long and 5 m wide. What is its perimeter?

    • A.135
    • B.37
    • C.64
    • D.59
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    Answer: C. 64

    2 × (27 + 5) = 64 m.

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37. 37. What is the area of a rectangle measuring 20 cm by 11 cm?

    • A.62
    • B.230
    • C.220
    • D.31
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    Answer: C. 220

    20 × 11 = 220 cm².

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38. 38. A square and a rectangle have the same perimeter of 40 cm. What is the area of the square?

    • A.80
    • B.90
    • C.100
    • D.110
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    Answer: C. 100

    Square's side = 40 ÷ 4 = 10 cm, so its area = 10 × 10 = 100 cm² (the rectangle's dimensions don't matter for this question).

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39. 39. A square field has perimeter 60 m. What is its area?

    • A.150
    • B.200
    • C.225
    • D.240
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    Answer: C. 225

    Side = 60 ÷ 4 = 15 m, area = 15 × 15 = 225 m².

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40. 40. The length of a rectangle is 3 times its breadth. If the breadth is 6 cm, what is the perimeter?

    • A.36
    • B.42
    • C.48
    • D.54
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    Answer: C. 48

    Length = 18 cm. Perimeter = 2 × (18 + 6) = 48 cm.

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41. 41. A square has side 12 cm. What is its perimeter?

    • A.48
    • B.36
    • C.144
    • D.52
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    Answer: A. 48

    4 × 12 = 48 cm.

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42. 42. A rectangle is 8 cm long and 9 cm wide. What is its area?

    • A.34
    • B.72
    • C.17
    • D.82
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    Answer: B. 72

    8 × 9 = 72 cm².

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43. 43. A square has side 6 cm. What is its perimeter?

    • A.24
    • B.18
    • C.28
    • D.36
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    Answer: A. 24

    4 × 6 = 24 cm.

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44. 44. What is the area of a rectangle measuring 19 cm by 9 cm?

    • A.28
    • B.181
    • C.171
    • D.56
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    Answer: C. 171

    19 × 9 = 171 cm².

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45. 45. What is the area of a rectangle measuring 13 cm by 10 cm?

    • A.130
    • B.46
    • C.140
    • D.23
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    Answer: A. 130

    13 × 10 = 130 cm².

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46. 46. What is the area of a square with side 16 cm?

    • A.32
    • B.64
    • C.256
    • D.260
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    Answer: C. 256

    16 × 16 = 256 cm².

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47. 47. What is the area of a rectangle measuring 24 cm by 7 cm?

    • A.168
    • B.62
    • C.31
    • D.178
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    Answer: A. 168

    24 × 7 = 168 cm².

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48. 48. A rectangle is 16 m long and 8 m wide. What is its perimeter?

    • A.40
    • B.128
    • C.48
    • D.32
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    Answer: C. 48

    2 × (16 + 8) = 48 m.

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49. 49. A rectangle is 19 m long and 6 m wide. What is its perimeter?

    • A.50
    • B.114
    • C.31
    • D.44
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    Answer: A. 50

    2 × (19 + 6) = 50 m.

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50. 50. Each small square in the grid shown represents 2 sq. cm. What is the total shaded area?

    • A.24
    • B.28
    • C.30
    • D.34
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    Answer: C. 30

    15 squares are shaded: 15 × 2 = 30 sq. cm.

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51. 51. A rectangular garden is 20 m long and 12 m wide. A path 2 m wide is built inside the garden, running all around the edge. What is the area of the path?

    • A.96
    • B.104
    • C.112
    • D.120
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    Answer: C. 112

    Outer area = 20×12 = 240 m². The remaining inner rectangle is 16×8 = 128 m² (each side shrinks by 2×2=4 m). Path area = 240 − 128 = 112 m².

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52. 52. The perimeter of a rectangle is 54 cm. Its length is twice its breadth. Find its area.

    • A.81
    • B.144
    • C.162
    • D.180
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    Answer: C. 162

    Let breadth = b, length = 2b. 2(2b+b) = 54, so 6b = 54, b = 9, length = 18. Area = 18 × 9 = 162 cm².

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53. 53. A rectangular room is 12 m by 8 m. What is the cost of carpeting it at ₹150 per m²?

    • A.₹12,000
    • B.₹13,800
    • C.₹14,400
    • D.₹15,000
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    Answer: C. ₹14,400

    Area = 12 × 8 = 96 m². Cost = 96 × 150 = ₹14,400.

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54. 54. A square sheet of side 20 cm has a smaller square of side 8 cm cut from one corner. What is the remaining area?

    • A.312
    • B.320
    • C.336
    • D.344
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    Answer: C. 336

    400 − 64 = 336 cm².

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55. 55. A rectangle is 10 cm long and 12 cm wide. What is its area?

    • A.22
    • B.130
    • C.44
    • D.120
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    Answer: D. 120

    10 × 12 = 120 cm².

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56. 56. A square has side 10 cm. What is its perimeter?

    • A.44
    • B.100
    • C.30
    • D.40
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    Answer: D. 40

    4 × 10 = 40 cm.

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57. 57. A square has side 17 cm. What is its perimeter?

    • A.289
    • B.72
    • C.68
    • D.51
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    Answer: C. 68

    4 × 17 = 68 cm.

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58. 58. A square has side 13 cm. What is its perimeter?

    • A.52
    • B.56
    • C.39
    • D.169
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    Answer: A. 52

    4 × 13 = 52 cm.

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59. 59. A rectangle is 15 cm long and 8 cm wide. What is its area?

    • A.23
    • B.46
    • C.130
    • D.120
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    Answer: D. 120

    15 × 8 = 120 cm².

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60. 60. What is the area of a rectangle measuring 16 cm by 9 cm?

    • A.154
    • B.50
    • C.144
    • D.25
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    Answer: C. 144

    16 × 9 = 144 cm².

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61. 61. A rectangle is 30 m long and 5 m wide. What is its perimeter?

    • A.150
    • B.70
    • C.65
    • D.40
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    Answer: B. 70

    2 × (30 + 5) = 70 m.

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62. 62. A rectangle is 23 m long and 13 m wide. What is its perimeter?

    • A.299
    • B.59
    • C.49
    • D.72
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    Answer: D. 72

    2 × (23 + 13) = 72 m.

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63. 63. What is the area of a rectangle measuring 17 cm by 7 cm?

    • A.119
    • B.129
    • C.48
    • D.24
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    Answer: A. 119

    17 × 7 = 119 cm².

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64. 64. A rectangle is 23 m long and 10 m wide. What is its perimeter?

    • A.230
    • B.56
    • C.43
    • D.66
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    Answer: D. 66

    2 × (23 + 10) = 66 m.

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65. 65. Fencing a square plot costs ₹40 per metre. If the total fencing cost is ₹6,400, what is the area of the plot?

    • A.1,200
    • B.1,400
    • C.1,600
    • D.1,800
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    Answer: C. 1,600

    Perimeter = 6400 ÷ 40 = 160 m. Side = 160 ÷ 4 = 40 m. Area = 40 × 40 = 1,600 m².

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