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Perimeter and Area – Class 6 Mathematics notes, important questions and MCQs

NCERT Class 6 Mathematics, chapter 6. Notes, key terms, important questions with answers and MCQs.

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Chapter overview

Perimeter is the distance around a shape; area is the surface it covers. Rectangles and squares have simple formulas.

Perimeter

  • Perimeter = sum of all sides.
  • Rectangle: 2(l + b); square: 4 × side; equilateral triangle: 3 × side.
  • Units: cm, m.

Area

  • Area = number of unit squares covering the shape.
  • Rectangle: l × b; square: side × side.
  • Units: cm², m². Shapes with the same perimeter can have different areas.

Key terms

Perimeter
total length of the boundary
Area
amount of surface enclosed
Square unit
unit of area, the area of a square of side 1 unit (cm², m²)

Formulas

  • Rectangle: P = 2(l + b), A = l × b
  • Square: P = 4a, A = a²

Important questions with answers

Find the perimeter of an equilateral triangle of side 7 cm.2 marks

Perimeter = 3 × 7 = 21 cm.

A rectangular room is 6 m long and 4 m wide. Find the cost of tiling the floor at ₹150 per m².3 marks

Area = 6 × 4 = 24 m². Cost = 24 × 150 = ₹3,600.

A rectangular park is 50 m long and 30 m wide. A 2 m wide path runs inside along its edges. Find the area of the path and the cost of laying it at ₹40 per m².5 marks

Area of park = 50 × 30 = 1,500 m². Inner rectangle = (50 − 4) × (30 − 4) = 46 × 26 = 1,196 m². Path area = 1,500 − 1,196 = 304 m². Cost = 304 × 40 = ₹12,160.

Quick revision

  • Perimeter in cm; area in cm².
  • Square: P = 4a.
  • Same perimeter ≠ same area.

Exam tips

  • Fencing needs perimeter; tiling or painting needs area.
  • Count half squares as ½ when finding area on squared paper.

Practice MCQs

  1. Perimeter of a square of side 5 cm is

    1. 10 cm
    2. 15 cm
    3. 25 cm
    4. 20 cm
    Show answer

    Answer: (d) 20 cm. 4 × 5.

  2. Area of a rectangle 6 cm by 4 cm is

    1. 10 cm²
    2. 20 cm²
    3. 24 cm²
    4. 48 cm²
    Show answer

    Answer: (c) 24 cm². 6 × 4.

  3. Perimeter of a rectangle 8 m by 3 m is

    1. 11 m
    2. 22 m
    3. 24 m
    4. 16 m
    Show answer

    Answer: (b) 22 m. 2(8 + 3).

  4. The side of a square with perimeter 36 cm is

    1. 6 cm
    2. 9 cm
    3. 12 cm
    4. 18 cm
    Show answer

    Answer: (b) 9 cm. 36 ÷ 4.

  5. A square has perimeter 36 cm. Its area is

    1. 36 cm²
    2. 144 cm²
    3. 9 cm²
    4. 81 cm²
    Show answer

    Answer: (d) 81 cm². Side 9 cm.

  6. How many 2 cm × 2 cm tiles cover a 10 cm × 8 cm board?

    1. 80
    2. 40
    3. 20
    4. 16
    Show answer

    Answer: (c) 20. 80 ÷ 4.

  7. A rectangle 9 cm × 4 cm and a square of side 6 cm have

    1. equal areas
    2. equal perimeters
    3. both equal
    4. neither equal
    Show answer

    Answer: (a) equal areas. Both 36 cm²; perimeters 26 and 24.

  8. A rectangle 12 m × 8 m is fenced 3 times around. Wire needed is

    1. 40 m
    2. 96 m
    3. 120 m
    4. 288 m
    Show answer

    Answer: (c) 120 m. Perimeter 40 m × 3.

All chapters of Class 6 Mathematics

Written by Kundali IQ from standard, well-established facts to help with revision. This is not an official NCERT publication; always read your textbook too.