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Chapter Analysis
Beginner22 pages • EnglishQuick Summary
Chapter 6 from the Class 6 NCERT Math textbook discusses the concepts of perimeter and area, focusing on how the perimeter is the total length around a closed figure, while area refers to the space enclosed within. It explains formulas for calculating the perimeter of rectangles, squares, and triangles, as well as the area of these shapes. Practice problems involve applying these formulas and understanding the relationship between different shapes' perimeters and areas.
Key Topics
- •Perimeter of polygons
- •Perimeter formulas for rectangles and squares
- •Area measurement
- •Area of rectangles and squares
- •Practical applications of perimeter and area
- •Relationship between perimeter and area
Learning Objectives
- ✓Understand how to calculate perimeter for different shapes
- ✓Apply formulas for finding area of rectangles and squares
- ✓Differentiate between perimeter and area
- ✓Relate practical problems to the concepts of perimeter and area
- ✓Develop a strategy for solving problems involving perimeter and area
Questions in Chapter
Find the missing terms: Perimeter of a rectangle = 14 cm; breadth = 2 cm; length = ?
Answer: length = 5 cm
Page 132
A rectangle having side lengths 5 cm and 3 cm is made using a piece of wire. If the wire is straightened and then bent to form a square, what will be the length of a side of the square?
Answer: Length of a side of square = 4 cm
Page 132
Find the length of the third side of a triangle having a perimeter of 55 cm and having two sides of length 20 cm and 14 cm, respectively?
Answer: Length of the third side of triangle = 21 cm
Page 132
Find the area of a rectangular garden 25 m long is 300 sq m. What is the width of the garden?
Answer: Width of the garden = 12 m.
Page 138
Additional Practice Questions
If a triangle has sides measuring 3 cm, 4 cm, and 5 cm, what is its perimeter?
easyAnswer: The perimeter is the sum of all sides: 3 cm + 4 cm + 5 cm = 12 cm.
How do you calculate the area of a triangle when the base is 5 cm and the height is 3 cm?
mediumAnswer: The area of a triangle = 1/2 × base × height = 1/2 × 5 cm × 3 cm = 7.5 sq cm.
If a square and a rectangle have the same area, but the square has a perimeter of 16 cm, what could be the dimensions of the rectangle if its length is 4 cm?
hardAnswer: The area of the square is side² = 4 cm × 4 cm = 16 sq cm. The rectangle, having area 16 sq cm and length 4 cm, will have a width of 4 sq cm. Therefore, its perimeter is 2 × (length + width) = 2 × (4 cm + 4 cm) = 16 cm.
A rectangle has a perimeter of 24 cm with a length of 7 cm. What is its width?
mediumAnswer: Perimeter = 2 × (length + width). Given, 24 cm = 2 × (7 cm + width) ⇒ 12 cm = 7 cm + width ⇒ width = 5 cm.
Explain how the concept of perimeter changes when adding or removing a part of a figure.
hardAnswer: Removing or adding a part to a figure often involves increasing or decreasing the total boundary length. Hence, perimeter changes as it is the total distance around the figure. For example, cutting a corner off a shape reduces its perimeter.