Introduction to Perimeter and Areas of Plane Figures Solutions Class 10 Chapter 17 from Vedantu
FAQs on RS Aggarwal Class 10 Solutions Chapter 17 Perimeter and Areas of Plane Figures
1. How should I approach solving problems from RS Aggarwal Class 10 Chapter 17, Perimeter and Areas of Plane Figures?
To effectively solve problems in this chapter, follow a structured approach. First, carefully read the question to identify the shapes involved (e.g., circle, square, triangle) and what you need to calculate (perimeter, area, shaded region). Next, list all the given values like radius, side length, or angle. Then, select the correct formula for each part of the problem. Execute the calculations step-by-step, ensuring you use the value of π (pi) as specified in the question (22/7 or 3.14). Finally, double-check your units (cm, m, cm², m²) in the final answer.
2. What is the step-by-step method to find the area of a shaded region combining a square and a circle?
Finding the area of a combined shaded region involves a subtraction method. Follow these steps:
Step 1: Identify the larger, encompassing shape and the smaller shape(s) removed from it. For instance, a circle inscribed in a square.
Step 2: Calculate the total area of the larger shape. For a square, use the formula Area = side².
Step 3: Calculate the area of the smaller, unshaded shape(s). For a circle, use Area = πr².
Step 4: Subtract the area of the smaller shape from the area of the larger shape. The result, Area of Shaded Region = Area (Larger Shape) - Area (Smaller Shape), is your answer.
3. What are the key concepts covered in RS Aggarwal Class 10 Chapter 17 for the 2025-26 session?
As per the latest syllabus, RS Aggarwal Chapter 17 primarily focuses on mensuration of plane figures. The key concepts include:
Calculating the circumference (perimeter) and area of a circle.
Finding the area of a sector of a circle using the angle (θ).
Determining the area of a segment of a circle (Area of Sector - Area of Triangle).
Solving problems on finding the areas of combined plane figures, which involve combinations of circles, squares, rectangles, and triangles.
4. How do you calculate the area of a major sector of a circle as per the methods in RS Aggarwal?
To calculate the area of a major sector, you first need the angle of the minor sector (θ). The angle of the major sector will be (360° - θ). The step-by-step method is:
Method 1: Use the formula for the area of a sector directly with the major angle: Area = ((360 - θ) / 360) * πr².
Method 2: Calculate the area of the entire circle (πr²) and subtract the area of the minor sector. Area of Major Sector = Area of Circle - Area of Minor Sector.
Both methods will yield the correct answer; choose the one that seems more direct based on the given information.
5. Why is it important to use the specific value of π (e.g., 22/7 or 3.14) mentioned in an RS Aggarwal problem?
Using the specified value of π is crucial for accuracy and scoring full marks. The choice is often intentional to simplify calculations. For example, if the radius or diameter is a multiple of 7, using π = 22/7 allows for easy cancellation and results in a precise integer or fractional answer. Using 3.14 in such cases can introduce decimal errors. Adhering to the value given in the question ensures your final answer matches the one expected by the examiner, which is critical in the CBSE evaluation pattern.
6. How does the concept of a 'segment' of a circle differ from a 'sector', and why does it change the calculation method?
The difference is fundamental to solving problems in this chapter. A sector is a pie-shaped region enclosed by two radii and the connecting arc. Its area is a fraction of the circle's total area. In contrast, a segment is the region enclosed by a chord and the connecting arc. This distinction completely changes the calculation. To find the area of a segment, you must first calculate the area of the corresponding sector and then subtract the area of the isosceles triangle formed by the two radii and the chord. This makes the segment calculation a multi-step process (Area of Segment = Area of Sector - Area of Triangle).
7. What is a common mistake to avoid when calculating the perimeter of a combined plane figure in Chapter 17?
A very common mistake is to simply add the perimeters of all the individual shapes. This is incorrect. The perimeter is the length of the outer boundary of the final, combined shape only. When shapes are joined, their common sides are no longer part of the outer boundary. For example, to find the perimeter of a shape made by a semicircle attached to a square, you must add the lengths of the three sides of the square and the length of the curved arc of the semicircle, not the full perimeter of the square and the full perimeter of the semicircle.
8. What is the correct formula to find the length of an arc of a sector with angle θ?
The length of an arc is a fraction of the total circumference of the circle. The correct formula, as used in RS Aggarwal solutions for problems related to perimeter, is: Length of Arc = (θ / 360°) * 2πr, where θ is the angle of the sector in degrees and r is the radius of the circle. This formula is essential for finding the perimeter of sectors or combined figures involving arcs.
