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RS Aggarwal Solutions

Class 8 RS Aggarwal Maths Area of a Trapezium and a Polygon Solutions - Free PDF Download

Class 8 RS Aggarwal Maths Area of a Trapezium and a Polygon Solutions - Free PDF Download

RS Aggarwal Maths Area of a Trapezium and a Polygon Solutions

The 18^th chapter in the Class 8 Maths syllabus is on Areas of Trapezium and Polygons. The fundamental properties of polygons and trapezium are explained in this chapter. The RS Aggarwal Class 8 Maths Chapter 18 solutions are available in PDF format and can be downloaded for free from Vedantu. The sums given in the exercise of this chapter are solved and explained in a stepwise manner in the RS Aggarwal Solutions Class 8 Chapter 18 PDF. These solutions are prepared by the highly experienced teachers at Vedantu according to the latest guidelines of CBSE.

By referring to these RS Aggarwal Solutions Class 8 Chapter 18 you will be able to understand the concepts of trapezium and polygons easily. Every solution in this PDF has been prepared using simple techniques so that you can understand and apply the concept related to it. Hence, download this PDF and learn how to solve different types of sums related to calculating the area of polygons and trapezium.

Vedantu is a platform that provides free NCERT Solution and other study materials for students. Download Class 8 Maths and Class 8 Science NCERT Solutions to help you to revise the complete syllabus and score more marks in your examinations.

Area of Trapezium: An Overview

The trapezium is a closed two-dimensional figure with two parallel sides. It is made up of four sides and four vertices. The trapezium's parallel sides are termed bases, while the non-parallel sides are called legs. Basic concepts:

The parallel sides of the trapezium are the bases, and the non-parallel sides are the legs.
The midpoint is a line drawn from the intersection of non-parallel sides.
The arrows and equal marks in the diagram indicate that the lines are parallel and that the lengths of the sides are equal.
If you cut the trapezium in half from the middle of the non-parallel sides, it will be separated into two unequal portions.
The two non-parallel sides of an isosceles trapezium are equal and produce equal angles on the bases.

Calculating the Area of Trapezium

The area of a trapezium is equal to half the sum of its parallel sides and height. The formula for the area of a trapezium is 12 × sum of parallel sides × times distance between them =12×(b1×b2)×h

The trapezium notion can be used in a variety of ways. In physics, it is used to solve numerous trapezium-related queries, whilst in mathematics, it is used to solve a variety of questions based on surface area or to find the complex figure area or perimeter. The trapezium formula can also be utilized in construction, as the roof shape is trapezoidal. It has a wide range of uses in everyday life.

RS Aggarwal Solutions for Class 8 Maths Chapter 18 Area of Trapezium and Polygons: RS Aggarwal Class 8 Chapter 18 Solution

After completing solving this chapter in the NCERT mathematics textbook, proceed to solve the questions of Class 8 RS Aggarwal Chapter 18. Students generally do it to grab more concepts related to this topic and get accustomed to different types of questions.

In the first exercise, the questions will focus on checking how you have learned to use the formulas described in this chapter. The preliminary questions will ask you to determine the area of trapeziums by just replacing the values of the terms in the formula. As you move forward, you will have to frame an equation to find out the unknown quantity cited in the questions. To solve these questions by framing the right equations, you will have to concentrate on learning the formulas. This will help you to replace the term with a variable and to form an equation. Follow the RS Aggarwal Solutions Class 8 Maths Ch 18 to learn how to formulate the answers easily.

In the same exercise, the hints will become more critical. You will have to focus on drawing the hints into a geometric figure to visualize the problem. It will help you solve the problem easily. As per the experts, drawing figures for geometric problems solves half of the problems. If you follow the RS Aggarwal Class 8 Maths Solutions Chapter 18, you will discover how the teachers have niftily used a diagram to make you understand the problem and to explain the solution.

You will be asked questions about quadrilaterals and polygons in the next exercise. The geometric figures in this case may or may not be regular. You'll need to focus on applying the basic formulas you learned earlier and in this chapter. You'll utilize the formulas for calculating triangle areas in most of the polygon-related problems. Proceed to tackle these problems one by one, and use RS Aggarwal Class 8 Solutions Maths Chapter 18 to answer your questions. You'll also notice that the formulae or expressions used to calculate a polygon's area are becoming increasingly complicated. Pay close attention to each term in the expression to prevent making errors.

In the next exercise, the questions will recall all the formulas you have learned regarding areas of different types of triangles, rhombus, and parallelograms. Recognize the geometric shapes and catch the hints so that you can use these formulas accordingly. Class 8 RS Aggarwal Chapter 18 is all about recapitulating all the area-based formulas and learning new ones. All the Exercise questions with solutions in Chapter-18 Area of a Trapezium and a Polygon are given below:

Exercise (Ex 18A) 18.1

Exercise (Ex 18A) 18.2

Exercise (Ex 18A) 18.3

Tips to Prepare Class 8 RS Aggarwal Chapter 18

You have now understood that this chapter focuses on teaching new area formulas of polygons and trapezium along with the recap of all the area formulas you have studied before. It is time to recall these formulas and jot down the new ones first. Learn how these formulas are determined so that you can understand the meaning of each term used.

Pay attention to the solution of every question in the exercises of RS Aggarwal Class 8 Maths Chapter 18 and learn how to use the new concepts. Practice using the solutions compiled by expert teachers.

FAQs on Class 8 RS Aggarwal Maths Area of a Trapezium and a Polygon Solutions - Free PDF Download

1. What is the step-by-step method to find the area of a trapezium as explained in RS Aggarwal Class 8 Maths Chapter 18 solutions?

The solutions for RS Aggarwal Class 8 Maths Chapter 18 consistently apply a clear, step-by-step method to find the area of a trapezium. The approach follows the standard formula and involves these steps:

Identify the parallel sides: First, identify the two parallel sides of the trapezium (often denoted as 'a' and 'b').
Determine the height: Next, identify the perpendicular distance between these parallel sides, which is the height ('h') of the trapezium.
Apply the formula: Substitute these values into the formula for the area of a trapezium, which is Area = 1/2 × (sum of parallel sides) × height.
Calculate the final answer: Perform the calculation to arrive at the final area, ensuring the unit is squared (e.g., cm², m²).

2. How do the RS Aggarwal solutions for Chapter 18 demonstrate finding the area of a complex polygon?

The solutions demonstrate a powerful technique for finding the area of any complex or irregular polygon. The method involves decomposing the polygon into simpler, standard shapes whose areas are easy to calculate. This is done by drawing one or more diagonals or perpendiculars. The polygon is typically broken down into a combination of:

Triangles
Rectangles
Trapeziums

The area of each of these simple shapes is calculated individually. Finally, the total area of the polygon is found by adding the areas of all these constituent shapes together.

3. Are the solutions for all exercises in Chapter 18, such as 18A, 18B, and 18C, available?

Yes, the RS Aggarwal solutions for Class 8 Maths Chapter 18 provide comprehensive, question-by-question solutions for all the exercises in the chapter. This includes detailed walkthroughs for problems in Exercise 18A, Exercise 18B, and Exercise 18C. Each solution is crafted to align with the CBSE 2025-26 curriculum guidelines, ensuring students understand the correct methodology for every problem type.

4. Why is it crucial to identify the correct 'height' of a trapezium, and how do the solutions clarify this?

Identifying the correct height is crucial because the area formula depends on the perpendicular distance between the parallel sides. A common mistake is to use the length of a slanted, non-parallel side as the height, which leads to an incorrect answer. The solutions clarify this by explicitly stating the height in each problem and often illustrating it in diagrams. This reinforces the concept that the height must form a right angle (90°) with the two parallel bases, regardless of how the trapezium is oriented.

5. How does the method for finding the area of a rhombus differ from that of a general quadrilateral in the Chapter 18 solutions?

The solutions in Chapter 18 showcase distinct methods based on the properties of the shapes.

For a rhombus, which is a special quadrilateral with equal sides and perpendicular diagonals, a specific formula is used: Area = 1/2 × (product of the lengths of the diagonals) or A = 1/2 × d₁ × d₂.
For a general quadrilateral, where diagonals may not be perpendicular, the method involves knowing the length of one diagonal and the lengths of the perpendiculars drawn to it from the opposite vertices. The area is then the sum of the areas of the two triangles formed by that diagonal.

The solutions carefully select the most efficient formula based on the given parameters for each shape.

6. What is the underlying principle for finding the area of any polygon by dividing it into simpler shapes?

The fundamental principle demonstrated in the solutions is the Area Addition Postulate. This mathematical concept states that the area of a whole figure is the sum of the areas of its non-overlapping parts. By breaking down a complex polygon (like a pentagon or hexagon) into familiar shapes such as triangles and trapeziums, we can calculate the area of each part separately. Since these parts do not overlap, adding their individual areas gives the exact total area of the original complex polygon. This method transforms a difficult problem into a series of simpler, manageable calculations.

7. What are the key formulas from Chapter 18 that a Class 8 student must master for exams?

Based on the problems solved in RS Aggarwal Chapter 18, a student must master the following key formulas for their exams:

Area of a Trapezium: 1/2 × (Sum of parallel sides) × Height
Area of a General Quadrilateral: 1/2 × Diagonal × (Sum of the heights of the two triangles formed)
Area of a Rhombus: 1/2 × (Product of its diagonals)

Mastering the application of these three formulas is essential for solving almost every question in this chapter.