Chapter 11: Area and Its Boundary

Math • Class 5

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Chapter Analysis

Beginner7 pages • English

Quick Summary

This chapter in Class 5 Math textbook covers the basic concepts of 'Area and its Boundary', focusing on how different shapes can have the same area but different perimeters. It involves storytelling and practical exercises to explore measuring areas using various methods, including guessing and checking with different objects. The theme emphasizes understanding how boundaries can change with shape despite the area remaining constant.

Key Topics

  • Understanding area and perimeter
  • Comparing areas of different shapes
  • Practical activities for measuring areas
  • Geometry of rectangles and circles
  • Effect of changing dimensions on area
  • Using real-life examples to explain concepts

Learning Objectives

  • Calculate the area and perimeter of simple geometric shapes.
  • Compare different shapes with equal areas.
  • Appreciate the relationship between shape and boundary.
  • Apply measurement concepts in practical situations.
  • Enhance estimation skills through exercises.
  • Understand real-world implications of geometric concepts.

Questions in Chapter

What other rectangles can he make with 100 metres of wire? Discuss which of these rectangles will have the biggest area.

Page 157

Sanya, Aarushi, Manav and Kabir made greeting cards. Complete the table for their cards.

Page 149

A square carrom board has a perimeter of 320 cm. How much is its area?

Page 149

How many tiles like the triangle given here will fit in the white design?

Page 149

Arbaz plans to tile his kitchen floor with green square tiles. Each side of the tile is 10 cm. His kitchen is 220 cm in length and 180 cm wide. How many tiles will he need?

Page 153

The fencing of a square garden is 20 m in length. How long is one side of the garden?

Page 153

A thin wire 20 centimetres long is formed into a rectangle. If the width of this rectangle is 4 centimetres, what is its length?

Page 153

Additional Practice Questions

If a rectangle has an area of 24 square meters and a length of 6 meters, what is its width?

easy

Answer: The width can be found by dividing the area by the length. Therefore, Width = 24 square meters / 6 meters = 4 meters.

How would the perimeter change if the sides of a square are doubled in length?

medium

Answer: If the sides of a square are doubled, the new perimeter will be twice the original perimeter because perimeter is proportional to the sum of the lengths of the sides.

Explore how the area of a circle changes as its diameter doubles.

hard

Answer: The area of a circle is proportional to the square of the radius (A = πr^2). If the diameter (and hence the radius) is doubled, the area becomes four times larger.

Create different rectangular configurations with a fixed perimeter of 20 cm and determine which has the largest area.

medium

Answer: The configuration where the rectangle is closest to a square (e.g., 5 cm x 5 cm) will have the largest area for a given perimeter.

Why would someone choose a circle over a rectangle when enclosing the maximum area for a given perimeter?

medium

Answer: A circle encloses the maximum area for a given perimeter due to its geometric properties, where all points are equidistant from the center.