Area and Its Boundary – Class 5 Maths Chapter 11 (NCERT)

Understanding Area and Perimeter

Area is the amount of flat space a shape covers. Imagine covering a shape completely with small unit squares (like 1 cm × 1 cm squares) — the number of squares needed is the area. Area is measured in square units, like square centimetres (sq cm) or square metres (sq m).

Perimeter (Boundary) is the total length of the outer line of a shape — it's like walking all the way around the edge of a park and measuring the distance you covered. Perimeter is measured in simple length units like cm or m, not square units.

A common confusion: area tells you 'how much space is inside,' while perimeter tells you 'how long is the fence around it.' Two shapes can have the same perimeter but different areas, and vice versa — this is a favourite CBSE exam trick, so always read the question carefully to check whether it asks for area or perimeter.

Key Terms You Must Know

Area

The amount of surface or flat space covered by a shape, measured in square units (sq cm, sq m).

Perimeter / Boundary

The total length of the outer boundary of a closed shape, measured in units of length (cm, m).

Square unit

A unit square of side 1 unit (e.g., 1 cm × 1 cm) used to measure area by counting.

Regular shape

A shape like a rectangle or square whose area can be found using a formula because all sides and angles follow a fixed pattern.

Irregular shape

A shape with an uneven boundary (like a leaf or a state map) whose area is estimated by counting squares on graph paper.

How to Find Area and Perimeter Step by Step

1. Step 1: Counting squares for irregular shapes — Draw or trace the shape on squared/graph paper. Count squares that are fully inside as 1 each. For squares that are more than half covered, count as 1. For squares exactly half covered, count as 1/2. Ignore squares less than half covered (count as 0). Add all values to get the total area in square units.
2. Step 2: Finding area of a rectangle using the formula — For a rectangle with length (l) and breadth (b), Area = l × b. Example: a rectangle of length 8 cm and breadth 5 cm has Area = 8 × 5 = 40 sq cm. This works because 8 rows of 5 unit squares each give 40 squares total.
3. Step 3: Finding area of a square — Since a square has all four sides equal, Area = side × side. Example: a square of side 6 cm has Area = 6 × 6 = 36 sq cm.
4. Step 4: Finding perimeter of any shape — Perimeter = sum of the lengths of all sides. For a rectangle, Perimeter = 2 × (length + breadth). For a square, Perimeter = 4 × side. Always add units correctly and double-check by walking through each side mentally.

Worked Examples

• Example 1: Find the area and perimeter of a rectangle with length 12 cm and breadth 7 cm.
  Step 1: Area = length × breadth = 12 × 7 = 84 sq cm.
  Step 2: Perimeter = 2 × (length + breadth) = 2 × (12 + 7) = 2 × 19 = 38 cm.
  Final answer: Area = 84 sq cm, Perimeter = 38 cm.

• Example 2: A square garden has each side measuring 15 m. Find its area and the length of fencing needed.
  Step 1: Area = side × side = 15 × 15 = 225 sq m.
  Step 2: Perimeter (fencing needed) = 4 × side = 4 × 15 = 60 m.
  Final answer: Area = 225 sq m; Fencing needed = 60 m.

• Example 3: On a graph paper, a leaf shape covers 10 full squares, 6 squares that are more than half filled, 4 squares exactly half filled, and 5 squares less than half filled. Find the area.
  Step 1: Full squares = 10, count as 10.
  Step 2: More-than-half squares = 6, count as 6.
  Step 3: Half squares = 4, count as 4 × 1/2 = 2.
  Step 4: Less-than-half squares = 5, count as 0.
  Step 5: Total area = 10 + 6 + 2 + 0 = 18 square units.
  Final answer: Area = 18 square units.

• Example 4: Two rectangles have the same perimeter of 20 cm. One has length 6 cm and breadth 4 cm; the other has length 8 cm and breadth 2 cm. Compare their areas.
  Step 1: Check perimeters: 2×(6+4)=20 cm and 2×(8+2)=20 cm — both equal, confirmed.
  Step 2: Area of first = 6 × 4 = 24 sq cm.
  Step 3: Area of second = 8 × 2 = 16 sq cm.
  Final answer: Same perimeter (20 cm) but different areas — 24 sq cm and 16 sq cm, showing area and perimeter are independent measures.

Common Mistakes and Board Exam Tips

• Do not confuse units: Area is always written in square units (sq cm, sq m), while Perimeter is in simple units (cm, m). Writing 'cm' for area is a very common mistake.
• Remember the counting rule for irregular shapes correctly: full square = 1, more than half = 1, exactly half = 1/2, less than half = 0. Skipping the half-square rule leads to wrong answers.
• For rectangles and squares, always identify length and breadth correctly before applying the formula — swapping them still gives the same area but can confuse perimeter calculations if sides are unequal.
• Two shapes can have equal perimeter but different area (and vice versa) — never assume they must match; CBSE often tests this concept directly.
• While finding perimeter, add all sides individually if the shape is irregular; don't apply the rectangle formula to non-rectangular shapes.

Practice Questions with Solutions

• Q: Find the area and perimeter of a rectangle with length 20 cm and breadth 9 cm.
  A: Step 1: Area = length × breadth = 20 × 9 = 180 sq cm.
  Step 2: Perimeter = 2 × (length + breadth) = 2 × (20 + 9) = 2 × 29 = 58 cm.
  Final answer: Area = 180 sq cm, Perimeter = 58 cm.

• Q: A square tile has a side of 4 cm. How many such tiles are needed to cover a rectangular floor of length 40 cm and breadth 24 cm?
  A: Step 1: Area of floor = 40 × 24 = 960 sq cm.
  Step 2: Area of one tile = 4 × 4 = 16 sq cm.
  Step 3: Number of tiles needed = 960 ÷ 16 = 60.
  Final answer: 60 tiles are needed.

• Q: On graph paper, a shape covers 8 full squares, 3 more-than-half squares, 2 exactly half squares, and 6 less-than-half squares. Find its area.
  A: Step 1: Full squares = 8, count as 8.
  Step 2: More-than-half squares = 3, count as 3.
  Step 3: Half squares = 2, count as 2 × 1/2 = 1.
  Step 4: Less-than-half squares = 6, count as 0.
  Final answer: Total area = 8 + 3 + 1 + 0 = 12 square units.

• Q: The perimeter of a square field is 48 m. Find the length of each side and the area of the field.
  A: Step 1: Perimeter = 4 × side, so side = Perimeter ÷ 4 = 48 ÷ 4 = 12 m.
  Step 2: Area = side × side = 12 × 12 = 144 sq m.
  Final answer: Each side = 12 m, Area = 144 sq m.

• Q: A rectangular park has an area of 300 sq m and a breadth of 15 m. Find its length and perimeter.
  A: Step 1: Area = length × breadth, so length = Area ÷ breadth = 300 ÷ 15 = 20 m.
  Step 2: Perimeter = 2 × (length + breadth) = 2 × (20 + 15) = 2 × 35 = 70 m.
  Final answer: Length = 20 m, Perimeter = 70 m.

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