Class 6 Maths: Measurement and Mensuration Ex 10.2 NCERT Guide

Welcome back, young mathematicians! In the previous section of Chapter 10, we mastered perimeter—the boundary of closed figures. Today, we step inside the boundary to explore Area. Area is the measure of the region enclosed by a closed figure. In NCERT Exercise 10.2, we learn a highly visual, hands-on way to estimate and calculate area using squared grid paper. This method is incredibly important because it helps us find the area of both regular shapes (like squares and rectangles) and irregular shapes (like leaves or star patterns) before we learn complex algebraic formulas. Let's open our YoLearn sketchpad, draw some grids, and master the rules of square counting!

Understanding Area via Grid Square Counting

To find the area of any closed shape on a squared paper, we count the number of unit squares enclosed by the figure. Each square on the grid has a side of length 1 unit, which means its area is exactly 1 square unit. However, shapes do not always align perfectly with the grid lines; some parts of the shape might only partially cover a square. To handle this, mathematicians have established a set of simple, intuitive convention rules. By applying these standard rules consistently, we can approximate the area of even highly complex, irregular figures with remarkable accuracy. This visual technique lays the foundation for understanding integrals and advanced geometry in higher classes.

The Four Golden Rules of Square Counting

Fully Filled Square: Any square on the grid that is completely covered inside the figure is counted as 1 full square unit.
More-Than-Half Filled Square: If more than half of a grid square lies inside the figure, we treat it as a fully filled square and count it as 1 square unit.
Exactly Half Filled Square: If a square is divided precisely in half by the boundary of the figure, we count it as exactly 1/2 (or 0.5) square unit.
Less-Than-Half Filled Square: Any grid square that has less than half of its area inside the figure is ignored completely. Its contribution is counted as 0 square units.

How to Calculate Area Step-by-Step

Trace and Identify — Trace the given shape carefully onto a centimetre squared paper (grid paper).
Count and Categorize — Look at each grid square covered by the shape. Classify them into four categories: Fully filled, More-than-half filled, Exactly half filled, and Less-than-half filled.
Calculate Individual Areas — Multiply the count of fully filled squares by 1, more-than-half filled by 1, exactly half-filled by 0.5, and ignore the less-than-half filled squares.
Sum Up for Total Area — Add all these values together to find the approximate total area. Always write the unit as 'square units' or 'sq units'.

YoLearn Exam Tips & Common Mistakes

Don't Forget the Units: A common mistake in exams is writing just a number (like '14'). Area is a two-dimensional measure, so always write the final answer with units, such as '14 square units' or '14 sq units'.
Double Counting Avoidance: Use a pencil to place a tiny tick mark (✓) in each grid square as you count it. This prevents you from counting any square twice or omitting squares entirely.
Symmetry Shortcut: If the figure is perfectly symmetrical, you can find the area of one half and simply multiply it by 2!

Practice Questions with Solutions

Q: Find the area of a closed region on a squared paper which contains 9 fully filled squares and 4 half-filled squares. A: Step 1: Write down the given counts of squares. - Number of fully filled squares = 9 - Number of exactly half-filled squares = 4 Step 2: Calculate the area contributed by each type. - Area from fully filled squares = 9 × 1 = 9 sq units - Area from half-filled squares = 4 × (1/2) = 2 sq units Step 3: Add the areas together. - Total Area = 9 + 2 = 11 sq units Final answer: 11 sq units
Q: A shape on grid paper covers 5 fully filled squares, 3 more-than-half filled squares, and 6 less-than-half filled squares. What is its estimated area? A: Step 1: Apply the golden rules of square counting. - Fully filled squares count as 1: 5 × 1 = 5 sq units - More-than-half filled squares count as 1: 3 × 1 = 3 sq units - Less-than-half filled squares count as 0: 6 × 0 = 0 sq units Step 2: Add all the calculated values. - Total Area = 5 + 3 + 0 = 8 sq units Final answer: 8 sq units
Q: An irregular leaf shape covers 12 fully filled squares, 4 more-than-half filled squares, 2 exactly half-filled squares, and 8 less-than-half filled squares. Calculate its total area. A: Step 1: Extract and convert the count for each category. - Fully filled: 12 squares → 12 × 1 = 12 sq units - More-than-half: 4 squares → 4 × 1 = 4 sq units - Half filled: 2 squares → 2 × (1/2) = 1 sq unit - Less-than-half: 8 squares → Ignored (0 sq units) Step 2: Sum the values. - Total Area = 12 + 4 + 1 = 17 sq units Final answer: 17 sq units
Q: Why is the area calculated using a grid paper called an 'estimated' or 'approximate' area? A: Step 1: Observe that irregular boundaries of a shape do not align perfectly with straight grid lines. Step 2: Because we approximate squares that are more-than-half filled as 1 full unit, and ignore those that are less-than-half filled, the mathematical values balance out closely, but are not perfectly exact. Final answer: The grid method is an approximation because we round partial squares to the nearest whole or half unit to simplify calculation.

Frequently Asked Questions

Can we write our answer in cm² if the grid is not specified?

If the grid size is not specified in the question, always write your answer as 'square units'. If the question states that it is a centimetre grid paper, then you can write your answer in square centimetres (sq cm or cm²).

What should I do if a square is exactly half-filled?

According to standard CBSE guidelines, exactly half-filled squares are assigned a value of 1/2 (or 0.5) square unit. You simply multiply the number of such half-filled squares by 0.5 and add it to your total.

How accurate is the grid counting method?

While it is an approximation, the grid counting method is highly reliable for finding the area of irregular surfaces because the overestimation from more-than-half filled squares usually balances out the underestimation from ignoring less-than-half filled squares.