Measurement and Mensuration Ex 10.3: NCERT Guide for Class 6 Maths

Welcome to the world of Mensuration! This chapter is all about measuring shapes. In the previous exercises, you learned about 'perimeter,' which is the distance around a shape. Now, in Exercise 10.3, we dive into a new, exciting concept called 'area.' Area is the amount of space a flat shape covers. Think about how much carpet you need for a room, or how much paint you need for a wall – that's all about area! It’s a super useful idea that we use in our daily lives all the time. In this guide, we will focus on finding the area of two very common shapes: rectangles and squares. You will master the simple formulas, learn how to apply them to real-world problems, and become confident in solving all the questions from your NCERT book. Let's start measuring!

What is Area?

Imagine you have a grid notebook. The perimeter of a shape you draw is like tracing the lines of the grid to form its boundary. The 'area', on the other hand, is the total number of small squares inside that boundary. Area measures the entire surface a shape covers.

Let's say you have a rectangle that is 5 squares long and 3 squares wide. To find its area, you can simply count all the squares inside it. You would find there are 15 squares in total. This gives us a clue about the formula! Instead of counting one by one, we can just multiply the length (5 squares) by the breadth (3 squares) to get 15 square units. This is why the unit for area is always a 'square unit', like square centimetre (cm²) or square metre (m²). We are essentially asking, "How many squares of 1 cm side, or 1 m side, can fit into this shape?"

Key Formulas for Area

Area of a Rectangle: The area of a rectangle is found by multiplying its length (l) by its breadth (b). Formula: Area = length × breadth or A = l × b.
Area of a Square: A square is a special rectangle where all sides are equal. So, its area is found by multiplying the side by itself. Formula: Area = side × side or A = side².

Solved Examples: Finding Area Step-by-Step

Example 1: Find the area of a rectangular park whose length is 40 metres and breadth is 25 metres. Step 1: Identify the shape and given values. The shape is a rectangle. Length (l) = 40 m Breadth (b) = 25 m Step 2: Write down the formula for the area of a rectangle. Area = length × breadth Step 3: Substitute the values into the formula and calculate. Area = 40 m × 25 m Area = 1000 Step 4: Write the final answer with the correct units. The area of the rectangular park is 1000 square metres (m²).
Example 2: A square carrom board has a side of 70 cm. What is its area? Step 1: Identify the shape and given value. The shape is a square. Side = 70 cm Step 2: Write down the formula for the area of a square. Area = side × side Step 3: Substitute the value into the formula and calculate. Area = 70 cm × 70 cm Area = 4900 Step 4: Write the final answer with the correct units. The area of the carrom board is 4900 square centimetres (cm²).

Important Points & Common Mistakes

Units are Key: Always write the units for area as 'square units' (e.g., cm², m², km²). Don't mix them up with the units for perimeter, which are just 'units' (cm, m, km).
Consistent Units: Before multiplying, make sure both length and breadth are in the same unit. If one is in metres and the other in centimetres, you must convert one of them first!
Area vs. Perimeter: Don't confuse the formulas. Area (l × b) measures the space inside. Perimeter (2 × (l + b)) measures the boundary.
Finding a Missing Side: If the area and one side are given, you can find the other side by dividing. For a rectangle, length = Area / breadth.

Practice Questions with Solutions

Q: A rectangular room is 4 m long and 3 m 50 cm wide. How many square metres of carpet is needed to cover the floor of the room? A: Step 1: Ensure all units are the same. The length is 4 m. The width is 3 m 50 cm. We know 100 cm = 1 m, so 50 cm = 0.50 m. The width is 3 + 0.50 = 3.5 m. Step 2: Use the formula for the area of a rectangle: Area = length × breadth. Step 3: Substitute the values: Area = 4 m × 3.5 m = 14 sq m. Final answer: 14 square metres of carpet is needed.
Q: A square park has a side of 50 m. A rectangular flower bed of size 10 m × 5 m is dug inside it. Find the area of the remaining part of the park. A: Step 1: Find the total area of the square park. Area of square = side × side = 50 m × 50 m = 2500 sq m. Step 2: Find the area of the rectangular flower bed. Area of rectangle = length × breadth = 10 m × 5 m = 50 sq m. Step 3: Subtract the area of the flower bed from the total area of the park. Remaining area = Area of park - Area of flower bed = 2500 sq m - 50 sq m = 2450 sq m. Final answer: The area of the remaining part of the park is 2450 sq m.
Q: The area of a rectangular garden is 300 sq m. If its length is 50 m, what is its width? A: Step 1: Write down the formula for area and the given values. Area = length × width. Area = 300 sq m, length = 50 m. Step 2: Rearrange the formula to find the width. Width = Area / length. Step 3: Substitute the values and calculate. Width = 300 sq m / 50 m = 6 m. Final answer: The width of the rectangular garden is 6 m.
Q: How many tiles whose length and breadth are 12 cm and 5 cm respectively will be needed to fit in a rectangular region whose length and breadth are 100 cm and 144 cm? A: Step 1: Find the area of the large rectangular region. Area_region = 100 cm × 144 cm = 14400 sq cm. Step 2: Find the area of one tile. Area_tile = 12 cm × 5 cm = 60 sq cm. Step 3: To find the number of tiles needed, divide the total area of the region by the area of one tile. Number of tiles = Area_region / Area_tile. Step 4: Calculate the result. Number of tiles = 14400 / 60 = 240. Final answer: 240 tiles will be needed.

Frequently Asked Questions

What is the difference between area and perimeter?

Perimeter is the total length of the boundary of a shape, like a fence around a garden. Area is the total amount of surface the shape covers, like the grass inside the garden. Perimeter is measured in units (cm, m), while area is measured in square units (cm², m²).

Why is the unit for area always squared (e.g., cm²)?

We measure area by figuring out how many small squares of a standard size (like 1 cm by 1 cm) can fit inside a shape. Because we are counting these 'unit squares', the unit is called a 'square centimetre' or cm².

How do I find the length of a rectangle if I know its area and breadth?

You can rearrange the area formula. The formula is Area = length × breadth. To find the length, you simply divide the area by the breadth: length = Area / breadth.