CBSE Class 8 Maths: Mensuration Exercise 11.1 Solutions & Concepts

Welcome to the world of Mensuration! This chapter is all about measuring geometric shapes. Think about the world around you – fencing a garden, painting a wall, or finding out how much carpet you need for a room. All of these tasks use mensuration! It’s a very practical part of maths that you’ll use throughout your life. In this section, we will focus specifically on Exercise 11.1 from your NCERT textbook. We will revisit and strengthen your understanding of two fundamental concepts: perimeter and area. You will learn the difference between them, how to calculate them for squares and rectangles, and how to apply these formulas to solve real-world problems. By the end of this lesson, you'll be able to confidently tackle any question from Mensuration Ex 11.1.

Key Concepts for Ex 11.1: Perimeter vs. Area

Before we dive into the problems, let's make sure we are crystal clear on the two main ideas in this exercise: Perimeter and Area.

Perimeter is the distance around a closed figure. Imagine you are walking along the edge of a park. The total distance you walk to complete one full round is the perimeter of the park. It's a measure of length. For a square with side 's', the perimeter is P = s + s + s + s = 4s. For a rectangle with length 'l' and breadth 'b', the perimeter is P = l + b + l + b = 2(l + b).

Area, on the other hand, is the amount of surface or space inside a closed figure. Imagine you are covering a floor with tiles. The total space the tiles cover is the area of the floor. It's a measure of a 2D surface. For a square with side 's', the area is A = s × s = s². For a rectangle with length 'l' and breadth 'b', the area is A = l × b.

A key difference is in their units. If the side of a square is in meters (m), its perimeter will also be in meters (m), but its area will be in square meters (m²).

Step-by-Step Guide to Solving Problems in Ex 11.1

  1. Step 1: Identify the Shape and Goal — Read the problem carefully. First, identify the geometric shape (e.g., square, rectangle). Then, determine what you need to find. Does the question ask for 'fencing', 'boundary', or 'length of tape'? That's Perimeter. Does it ask for 'covering a surface', 'ploughing a field', or 'space occupied'? That's Area.
  2. Step 2: List the Given Information — Write down all the measurements provided in the question. This could be the length of a side, the length and breadth, or sometimes the total perimeter or area itself.
  3. Step 3: Choose the Correct Formula — Based on the shape and your goal (perimeter or area), select the right formula. - Perimeter of Square: P = 4 × side - Area of Square: A = side × side - Perimeter of Rectangle: P = 2 × (length + breadth) - Area of Rectangle: A = length × breadth
  4. Step 4: Calculate and State the Units — Substitute the known values into your chosen formula and calculate the answer. Don't forget the final, most important part: write the answer with the correct units! Use units like cm, m for perimeter, and cm², m² for area.

Exam Tip: Avoid These Common Errors

When solving mensuration problems, students often make a few common mistakes. Be careful about these points to score full marks!

  1. Confusing Formulas: Don't mix up the formula for perimeter and area. Remember, perimeter is about adding lengths (4s or 2(l+b)), while area is about multiplying them (s² or l×b).
  2. Incorrect Units: This is a very common error! Always write the units. Perimeter is a length, so its units are m, cm, etc. Area is a surface, so its units are m², cm², etc. Writing '50 m' for an area answer is incorrect.
  3. Finding Side from Area: To find the side of a square from its area, you must find the square root, not divide by 4. For example, if Area = 36 m², the side is √36 = 6 m, not 36/4 = 9 m.

Practice Questions with Solutions

  • Q: A rectangular field is 60 m long and 40 m wide. Find its area and perimeter. A: Step 1: Calculate the area. Area = Length × Width = 60 m × 40 m = 2400 m². Step 2: Calculate the perimeter. Perimeter = 2 × (Length + Width) = 2 × (60 m + 40 m) = 2 × 100 m = 200 m. Final answer: Area = 2400 m², Perimeter = 200 m.
  • Q: A square park has a side of 70 m. A rectangular park has a length of 100 m and a width of 49 m. Which park has a larger area? A: Step 1: Calculate the area of the square park. Area_square = Side × Side = 70 m × 70 m = 4900 m². Step 2: Calculate the area of the rectangular park. Area_rectangle = Length × Width = 100 m × 49 m = 4900 m². Step 3: Compare the areas. Both parks have the same area. Final answer: Both parks have the same area of 4900 m².
  • Q: The area of a rectangular plot is 500 m². If its length is 25 m, find its width and perimeter. A: Step 1: Find the width. Area = Length × Width ⇒ 500 m² = 25 m × Width ⇒ Width = 500/25 = 20 m. Step 2: Calculate the perimeter. Perimeter = 2 × (Length + Width) = 2 × (25 m + 20 m) = 2 × 45 m = 90 m. Final answer: Width = 20 m, Perimeter = 90 m.
  • Q: A rectangular floor is 8 m long and 6 m wide. It costs Rs 25 per square meter to tile the floor. Find the total cost of tiling. A: Step 1: Calculate the area of the floor. Area = Length × Width = 8 m × 6 m = 48 m². Step 2: Calculate the total cost. Total Cost = Area × Cost per m² = 48 m² × Rs 25/m² = Rs 1200. Final answer: The total cost of tiling is Rs 1200.

Frequently Asked Questions

What is the main difference between perimeter and area?

Perimeter is the length of the boundary of a 2D shape, like the length of a fence around a garden. Area is the amount of space inside that boundary, like the amount of grass inside the garden. Perimeter is measured in units like m or cm, while area is measured in square units like m² or cm².

How do I know whether to calculate perimeter or area in a word problem?

Look for keywords. If the problem talks about 'fencing', 'boundary', 'distance around', or 'framing', you need to calculate the perimeter. If it talks about 'covering a surface', 'carpeting a room', 'painting a wall', or 'space occupied', you need to calculate the area.

If a square and a rectangle have the same perimeter, which one has a larger area?

For a fixed perimeter, the square will always have a larger area than any rectangle with the same perimeter. This is a key concept explored in Exercise 11.1.