RS Aggarwal Solutions Class 6 Chapter-21 Concept of Perimeter and Area (Ex 21A) Exercise 21.1 - Free PDF
FAQs on RS Aggarwal Solutions Class 6 Chapter-21 Concept of Perimeter and Area (Ex 21A) Exercise 21.1
1. How do the RS Aggarwal solutions for Class 6 Maths Chapter 21 explain the concept of perimeter?
The solutions for this chapter explain that the perimeter is the total distance around the boundary of a closed two-dimensional figure. It is calculated by adding the lengths of all its sides. For any polygon, the perimeter is the sum of the lengths of its line segments, representing the total length of its outline.
2. What is the correct method to find the perimeter of different shapes like squares, rectangles, and triangles in Exercise 21.1?
The correct method involves using specific formulas for each shape, which simplifies the calculation process. The key formulas are:
- Perimeter of a Rectangle: 2 × (length + breadth)
- Perimeter of a Square: 4 × length of one side
- Perimeter of a Triangle: Sum of all three sides (side a + side b + side c)
- Perimeter of an Equilateral Triangle: 3 × length of one side
3. How do you solve problems where the perimeter is given, but you need to find a missing side length?
To find a missing side length when the total perimeter is known, you need to work backwards using the perimeter formula. First, write down the formula for the shape. Then, substitute the known values for the perimeter and the given side lengths. Finally, solve the resulting algebraic equation for the unknown side. For a rectangle, if the perimeter and length are known, the formula becomes: Breadth = (Perimeter / 2) - Length.
4. What is the step-by-step process for solving word problems involving the cost of fencing a field, as shown in Exercise 21.1?
To solve such problems methodically, you should follow these steps:
- First, calculate the perimeter of the field using the given dimensions. The perimeter represents the total length of fencing required.
- Next, identify the cost of fencing per unit length (e.g., per metre) from the problem statement.
- Finally, multiply the total perimeter by the cost per unit length to find the total cost of fencing. The formula is: Total Cost = Perimeter × Rate per metre.
5. What shapes are covered in the problems for RS Aggarwal Class 6 Chapter 21, Exercise 21.1?
Exercise 21.1 primarily focuses on calculating the perimeter of various common polygons. The key shapes included in the problems are triangles (including scalene, isosceles, and equilateral triangles), rectangles, and squares. The exercises build a foundational understanding of how to apply perimeter formulas to these fundamental geometric figures.
6. What is the fundamental difference between perimeter and area for a Class 6 student?
The fundamental difference is what they measure. Perimeter measures the length of the outer boundary of a shape (a one-dimensional measure, like a fence) and is expressed in units like metres (m) or centimetres (cm). In contrast, area measures the amount of flat space a shape covers inside its boundary (a two-dimensional measure, like a carpet) and is expressed in square units, such as square metres (m²) or square centimetres (cm²).
7. Why is it important to use consistent units (like cm, m) when solving perimeter problems in this chapter?
Using consistent units is crucial for accuracy and real-world meaning. If the sides of a shape are given in different units (e.g., length in metres and breadth in centimetres), you must convert them to the same unit before applying the perimeter formula. Mixing units without conversion will lead to a mathematically incorrect answer that does not represent the actual physical length of the boundary.
8. How does understanding perimeter in Chapter 21 help in solving real-life problems beyond the textbook?
Understanding perimeter is a practical skill with many real-world applications. For instance, you use this concept when you need to:
- Calculate the amount of fencing needed for a garden or plot of land.
- Determine the length of a decorative border for a photo frame or a room.
- Measure the distance covered when jogging around a rectangular park.
