Class 6 Maths Perimeter and Area Notes

Class 6 Maths – Chapter: Perimeter and Area

1. Introduction

• Perimeter: The distance around a closed figure.
  Formula depends on the shape.
  • Rectangle: P = 2 × (Length + Breadth)
  • Square: P = 4 × Side
  • Triangle: P = Sum of all three sides
  • Circle: Circumference C = 2 × π × r
• Area: The surface enclosed within a figure.
  • Rectangle: A = Length × Breadth
  • Square: A = Side × Side
  • Triangle: A = ½ × Base × Height
  • Parallelogram: A = Base × Height
  • Circle: A = π × r²

---

2. Important Notes

1. Perimeter is measured in linear units (cm, m, km).
2. Area is measured in square units (cm², m², km²).
3. Perimeter of irregular shapes = sum of all sides.
4. Conversion:
   • 1 m² = 10,000 cm²
   • 1 km² = 1,000,000 m²

---

3. Examples

Example 1 – Rectangle:

• Length = 10 m, Breadth = 5 m
• Perimeter = 2 × (10 + 5) = 30 m
• Area = 10 × 5 = 50 m²

Example 2 – Square:

• Side = 6 cm
• Perimeter = 4 × 6 = 24 cm
• Area = 6 × 6 = 36 cm²

Example 3 – Triangle:

• Sides = 5 cm, 6 cm, 7 cm
• Perimeter = 5 + 6 + 7 = 18 cm
• Base = 6 cm, Height = 4 cm
• Area = ½ × 6 × 4 = 12 cm²

Example 4 – Circle:

• Radius r = 7 cm
• Circumference = 2 × π × 7 ≈ 44 cm
• Area = π × 7² ≈ 154 cm²

---

4. Mixed Practice Questions (50 Questions)

Part A – Multiple Choice Questions (MCQs) – 15 Questions

1. Perimeter of a square with side 8 cm is:
   a) 32 cm
   b) 16 cm
   c) 64 cm
   d) 24 cm
2. Area of a rectangle with length 10 m and breadth 5 m is:
   a) 50 m²
   b) 15 m²
   c) 30 m²
   d) 100 m²
3. Circumference of a circle with radius 7 cm (use π = 22/7) is:
   a) 44 cm
   b) 154 cm
   c) 22 cm
   d) 28 cm
4. Area of a triangle with base 6 cm and height 4 cm is:
   a) 12 cm²
   b) 10 cm²
   c) 24 cm²
   d) 18 cm²
5. Perimeter of a rectangle is 30 cm. If length = 8 cm, breadth = ?
   a) 7 cm
   b) 6 cm
   c) 5 cm
   d) 10 cm
6. Area of a square = 49 cm². Side = ?
   a) 7 cm
   b) 14 cm
   c) 49 cm
   d) 21 cm
7. Circumference of a circle = 2πr. If r = 5 cm, circumference = ?
   a) 25π cm
   b) 10π cm
   c) 5π cm
   d) 2π cm
8. Perimeter of an equilateral triangle with side 6 cm = ?
   a) 12 cm
   b) 18 cm
   c) 24 cm
   d) 36 cm
9. Area of a parallelogram = Base × Height. Base = 8 cm, Height = 5 cm. Area = ?
   a) 40 cm²
   b) 13 cm²
   c) 20 cm²
   d) 45 cm²
10. Area of a rectangle with length = breadth = 6 cm is:
    a) 12 cm²
    b) 36 cm²
    c) 18 cm²
    d) 24 cm²
11. Which is measured in linear units?
    a) Area
    b) Perimeter
    c) Volume
    d) Mass
12. Which is measured in square units?
    a) Perimeter
    b) Area
    c) Circumference
    d) Length
13. Perimeter of circle is also called:
    a) Radius
    b) Diameter
    c) Circumference
    d) Area
14. Area of circle formula:
    a) π × r²
    b) 2 × π × r
    c) r² × 2
    d) π × d²
15. Area of square = 100 cm². Side = ?
    a) 10 cm
    b) 20 cm
    c) 50 cm
    d) 25 cm

---

Part B – Fill in the Blanks – 10 Questions

16. Perimeter is the __________ around a figure.
17. Area is the __________ of a figure.
18. Perimeter of square = __________ × Side
19. Area of rectangle = __________ × __________
20. Circumference of circle = __________
21. Area of circle = __________
22. Base of triangle = 10 cm, height = 6 cm, Area = __________ cm²
23. Perimeter of rectangle = 2 × (__________ + __________)
24. Square with side 9 cm, Area = __________ cm²
25. Radius = 7 cm, Area of circle = __________ cm²

---

Part C – True/False – 5 Questions

26. Area is measured in linear units. (False)
27. Perimeter is measured in linear units. (True)
28. Perimeter of a circle = 2 × π × r. (True)
29. Area of a triangle = Base × Height. (False)
30. Area of square = Side × Side. (True)

---

Part D – Match the Following – 5 Questions

Column A	Column B
31. Perimeter of rectangle	a) 4 × Side
32. Area of square	b) Base × Height
33. Circumference of circle	c) 2 × (L + B)
34. Area of triangle	d) π × r²
35. Perimeter of square	e) 2 × π × r

---

Part E – Short Answer / Problem Solving – 15 Questions

36. Perimeter of rectangle: Length = 12 cm, Breadth = 8 cm.
37. Area of rectangle: Length = 15 m, Breadth = 10 m.
38. Perimeter of square with side 9 cm.
39. Area of square with side 7 cm.
40. Circumference of circle: r = 14 cm, π = 22/7
41. Area of circle: r = 3.5 cm, π = 22/7
42. Area of triangle: Base = 8 cm, Height = 6 cm
43. Perimeter of triangle: Sides = 5 cm, 6 cm, 7 cm
44. Area of parallelogram: Base = 12 m, Height = 8 m
45. Find side of square if perimeter = 36 cm
46. Find length of rectangle if perimeter = 50 m, breadth = 10 m
47. Find breadth of rectangle if area = 60 m², length = 12 m
48. A triangular field has base = 50 m, height = 30 m. Find area
49. A circular pond has radius = 7 m. Find circumference and area
50. A rectangular garden has length = 20 m, breadth = 15 m. Find perimeter and area

Answers – Class 6 Maths: Perimeter and Area

---

Part A – MCQs (Answers)

1. a) 32 cm → 4 × 8 = 32
2. a) 50 m² → 10 × 5 = 50
3. a) 44 cm → 2 × π × 7 = 2 × 22/7 × 7 = 44
4. a) 12 cm² → ½ × 6 × 4 = 12
5. b) 7 cm → 2 × (8 + B) = 30 → 16 + 2B = 30 → 2B = 14 → B = 7
6. a) 7 cm → √49 = 7
7. b) 10π cm → 2 × π × 5 = 10π
8. b) 18 cm → 3 × 6 = 18
9. a) 40 cm² → 8 × 5 = 40
10. b) 36 cm² → 6 × 6 = 36
11. b) Perimeter
12. b) Area
13. c) Circumference
14. a) π × r²
15. a) 10 cm → √100 = 10

---

Part B – Fill in the Blanks (Answers)

16. Distance around a figure
17. Surface inside a figure
18. 4 × Side
19. Length × Breadth
20. 2 × π × r
21. π × r²
22. ½ × 10 × 6 = 30 cm²
23. Length + Breadth
24. 9 × 9 = 81 cm²
25. π × 7² ≈ 154 cm²

---

Part C – True/False (Answers)

26. False
27. True
28. True
29. False (Correct: ½ × Base × Height)
30. True

---

Part D – Match the Following (Answers)

Column A	Column B
31. Perimeter of rectangle	c) 2 × (L + B)
32. Area of square	a) 4 × Side
33. Circumference of circle	e) 2 × π × r
34. Area of triangle	b) Base × Height ÷ 2
35. Perimeter of square	a) 4 × Side

---

Part E – Short Answer / Problem Solving (Answers)

36. Perimeter of rectangle: 2 × (12 + 8) = 2 × 20 = 40 cm
37. Area of rectangle: 15 × 10 = 150 m²
38. Perimeter of square: 4 × 9 = 36 cm
39. Area of square: 7 × 7 = 49 cm²
40. Circumference of circle: 2 × π × 14 = 2 × 22/7 × 14 = 88 cm
41. Area of circle: π × 3.5² ≈ 22/7 × 12.25 ≈ 38.5 cm²
42. Area of triangle: ½ × 8 × 6 = 24 cm²
43. Perimeter of triangle: 5 + 6 + 7 = 18 cm
44. Area of parallelogram: 12 × 8 = 96 m²
45. Side of square: 36 ÷ 4 = 9 cm
46. Length of rectangle: 2 × (L + 10) = 50 → 2L + 20 = 50 → 2L = 30 → L = 15 m
47. Breadth of rectangle: Area = L × B → 60 ÷ 12 = 5 m
48. Area of triangular field: ½ × 50 × 30 = 25 × 30 = 750 m²
49. Circular pond:

• Circumference = 2 × π × 7 = 44 m
• Area = π × 7² = 154 m²

50. Rectangular garden:

• Perimeter = 2 × (20 + 15) = 2 × 35 = 70 m
• Area = 20 × 15 = 300 m²