How Many Squares: CBSE Class 5 Maths Chapter 3

Understanding Area by Counting Squares

Imagine you have a chocolate bar made of small square pieces. The total number of square pieces in the bar is its area. In maths, Area is the total amount of surface a flat shape covers. The easiest way to measure this is to see how many squares of a fixed size can fit inside it.

Let's say we have a square grid paper, where each little square is 1 centimetre long and 1 centimetre wide. The area of one such square is 1 square centimetre, which we write as 1 sq cm.

Now, if you draw a rectangle on this grid that is 4 cm long and 3 cm wide, how many of these little squares would it cover? You can simply count them! You would find 12 squares inside. So, the area of the rectangle is 12 sq cm.

There's also a magic shortcut! Instead of counting every single square, you can multiply the length and the breadth. For our rectangle: Length = 4 cm, Breadth = 3 cm. Area = 4 × 3 = 12 sq cm. It's the same answer! This formula, Area = Length × Breadth, works for all rectangles and squares and is a super useful tool.

What is Perimeter?

While area measures the space inside a shape, Perimeter measures the distance around the shape. Think of it like walking along the boundary line of a park. The total distance you walk to come back to your starting point is the perimeter of the park.

To find the perimeter of a shape on a grid paper, you just need to add up the lengths of all its sides. If a rectangle has a length of 5 cm and a breadth of 3 cm, its sides are 5 cm, 3 cm, 5 cm, and 3 cm.

So, the Perimeter = 5 + 3 + 5 + 3 = 16 cm.

A faster way for rectangles is to use the formula: Perimeter = 2 × (Length + Breadth).
Let's try it: Perimeter = 2 × (5 + 3) = 2 × 8 = 16 cm. See? It works perfectly! Remember, perimeter is a length, so its unit is cm, m, etc., not sq cm.

How to Find the Area of Irregular Shapes

1. Step 1: Count the Complete Squares — First, look at the shape drawn on the square grid. Count all the squares that are fully inside the boundary of the shape. Let's call this number 'F'.
2. Step 2: Count Squares More Than Half-Filled — Next, find the squares that are not complete but are more than half-filled. Count them and treat each one as a full square. Let's call this number 'M'.
3. Step 3: Count Exactly Half-Filled Squares — Now, count the squares that are exactly half-filled. Take every two of these half-squares as one full square. So, divide the count of half-squares by 2. Let's call this number 'H'.
4. Step 4: Ignore Less Than Half-Filled Squares — Finally, any square that is less than half-filled should be ignored. We don't count them.
5. Step 5: Calculate the Total Approximate Area — The approximate area of the shape is the sum of the counts from the first three steps. Total Area ≈ F + M + (H / 2).

Area vs. Perimeter: Key Differences

• Measurement: Area measures the space inside a shape. Perimeter measures the length of the boundary around a shape.
• Units: Area is measured in square units (like sq cm, sq m). Perimeter is measured in linear units (like cm, m).
• Same Perimeter, Different Area: Two shapes can have the same perimeter but different areas. A rectangle of 6 cm x 2 cm has a perimeter of 16 cm and area of 12 sq cm. A square of 4 cm x 4 cm also has a perimeter of 16 cm, but its area is 16 sq cm!
• Same Area, Different Perimeter: Two shapes can have the same area but different perimeters. A rectangle of 4 cm x 3 cm has an area of 12 sq cm and perimeter of 14 cm. A rectangle of 6 cm x 2 cm also has an area of 12 sq cm, but its perimeter is 16 cm.

Practice Questions with Solutions

• Q: A rectangle is drawn on a 1 cm grid paper. Its length is 7 cm and its breadth is 4 cm. What is its area and perimeter?
  A: Step 1: Find the area using the formula Area = Length × Breadth.
  Area = 7 cm × 4 cm = 28 sq cm.
  Step 2: Find the perimeter using the formula Perimeter = 2 × (Length + Breadth).
  Perimeter = 2 × (7 cm + 4 cm) = 2 × 11 cm = 22 cm.
  Final answer: The area is 28 sq cm and the perimeter is 22 cm.

• Q: A leaf is placed on a 1 cm square grid. It covers 15 full squares, 8 squares that are more than half-filled, 6 squares that are exactly half-filled, and 10 squares that are less than half-filled. What is the approximate area of the leaf?
  A: Step 1: Count the full squares. Number of full squares = 15.
  Step 2: Count the squares that are more than half-filled. We treat these as full squares. Number of 'more-than-half' squares = 8.
  Step 3: Count the half-filled squares and find their contribution to the area. Number of half-filled squares = 6. Area from these = 6 / 2 = 3 sq cm.
  Step 4: Add the areas from each step. We ignore the less-than-half squares. Approximate Area = 15 + 8 + 3 = 26 sq cm.
  Final answer: The approximate area of the leaf is 26 sq cm.

• Q: Ram has a rectangular field of length 10 m and breadth 8 m. Shyam has a square field of side 9 m. Whose field has a larger area?
  A: Step 1: Calculate the area of Ram's field.
  Area = Length × Breadth = 10 m × 8 m = 80 sq m.
  Step 2: Calculate the area of Shyam's field. For a square, Length = Breadth = side.
  Area = Side × Side = 9 m × 9 m = 81 sq m.
  Step 3: Compare the two areas. 81 sq m is greater than 80 sq m.
  Final answer: Shyam's field has a larger area.

• Q: Two rectangles, A and B, both have an area of 24 sq cm. Rectangle A has a length of 6 cm. Rectangle B has a length of 8 cm. Which rectangle has a greater perimeter?
  A: Step 1: Find the breadth and perimeter of Rectangle A.
  Area = L × B => 24 = 6 × B => Breadth = 24 / 6 = 4 cm.
  Perimeter A = 2 × (6 + 4) = 2 × 10 = 20 cm.
  Step 2: Find the breadth and perimeter of Rectangle B.
  Area = L × B => 24 = 8 × B => Breadth = 24 / 8 = 3 cm.
  Perimeter B = 2 × (8 + 3) = 2 × 11 = 22 cm.
  Step 3: Compare the perimeters. Perimeter B (22 cm) is greater than Perimeter A (20 cm).
  Final answer: Rectangle B has a greater perimeter.

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