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NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals - PDF Download

JEE Mains & Advanced

NCERT solutions for class 8 maths chapter 3 Understanding Quadrilaterals defines a polygon by the fact that it is a closed curve composed of straight lines. So a quadrilateral is a polygon shape with four sides, four angles, and four vertices. In this chapter, you will be introduced to some fundamental concepts that they will need to be familiar with before progressing to the next step in their quadrilateral studies. These concepts include classifying polygons based on their sides, exploring diagonals and concave polygons, convex polygons, regular polygons, irregular polygons, and angle sum properties.

NCERT solutions for class 8 maths chapter 3 Understanding Quadrilaterals has several properties, different types of quadrilaterals and concepts. This chapter also includes types of questions and exercises to give a thorough understanding of topics and concepts.

eSaral's mathematics experts have prepared NCERT solutions for class 8 maths chapter 3 Understanding Quadrilateral from an examination perspective. These solutions elucidate the precise manner in which the problems are resolved. By comprehending the concepts used in NCERT solutions class 8, students can eliminate any doubts they may have regarding the chapter. Students can easily download NCERT solutions class 8 maths chapter 3 Understanding Quadrilaterals PDF for free from eSaral website. The experts of maths teachers discuss all questions based on NCERT guidelines. When students answer the exercise questions, they will be able to understand the topic better and more easily.

Important Topics covered in Chapter 3 - Understanding Quadrilaterals

There are many sections and topics dealing with the various elements of chapter 3 Understanding Quadrilaterals. Here, we will discuss the most essencial topics of chapter 3.

3.1 Introduction

3.1.1 Convex and Concave Polygons

3.1.2 Regular and Irregular Polygons

3.2 Sum of the Measures of the Exterior Angles of a Polygons

3.3 Kinds of Quadrilaterals

3.3.1 Trapezium

3.3.2 Kite

3.3.3 Parallelogram

3.3.4 Elements of a Parallelogram

3.3.5 Angles of a Parallelogram

3.3.6 Diagonals of a Parallelogram

3.4 Some Special Parallelograms

3.4.1 Rhombus

3.4.2 A rectangle

3.4.3 A square

3.1 Introduction - Paper is a model of a plane surface. A plane curve is formed by connecting several points without taking a pencil away from the paper. Another type of polygon is a quadrilateral. Quadrilaterals have four sides, four vertices, four angles, and two diagonals. There are different types of planes developed for NCERT class 8 mathematics chapter 3.

              3.1.1 Convex and Concave Polygons - A convex polygon does not have any parts of its diagonals in its exterior, nor does it have any line segments joining any two points in the polygon's interior that are entirely inside the polygon. In other words, the angles of convex polygons are less than 180 degrees. Concave polygons are more than 180 degrees. To know the fundamental difference between the two, students can check the NCERT solutions for class 8 math chapter 3.

             3.1.2 Regular and Irregular Polygons - A regular polygon is a polygon that is both equiangular and equilateral. For example, a square is a polygon whose sides have the same length and have the same angles. This makes it a regular polygon. A rectangle is equiangular, but note equilateral

3.2 Sum of the Measures of the Exterior Angles of a Polygon - A polygon is a closed two-dimensional representation consisting of three or more linear segments. The line segments of a polygon are referred to as the sides of the polygons. A vertex is the point where two vertices intersect. An interior angle is the angle formed between two vertices that are adjacent to each other. exterior angle is the angle outside the enclosure of the polygon by one of its sides and the extension on its adjacent side. 

3.3 Kinds of Quadrilaterals - A quadrilateral has different lengths of sides and different angles for different measures. However, a square, rectangle, etc. has all sides of a quadrilateral and all angles are equal. This means that the area of a quadrilateral depends on the type of the quadrilateral.

Quadrilaterals are named according to their sides or angles. Some of the types of quadrilaterals developed by NCERT for Class 8 Maths Chapter 3 are:

            3.3.1 Trapezium - A convex trapezium quadrilateral has exactly one pair of opposite sides parallel to each other. A trapezium is 2-dimensional. When drawn on paper, a trapezium looks like a table. In Euclidean geometry, a quadrilateral is a polygon with four sides and four vertices. 

There are many ways to see trapezium in practice. One of the most important uses of trapezium is in the form of the trapezium rule. This rule states that the area under a curve should be divided into several trapeziums, and then the area of each of these trapeziums should be evaluated. If you want to know the basic formulas and structure of trapezium, you can check NCERT solutions for class 8 math chapter 3.

           3.3.2 Kite - Polygon is a closed figure of a plane defined by a finite number of line segments. A quadrilateral is a polygon with four sides. 360 degree is the sum of interior angles in a Quadrilateral. It's the number of diagonals in an N-sided Polygon. A quadrilateral thus has two diagonals. The sum of all of the exterior angles of any n polygon is always 360. A kite is a quadrilateral shape in which two adjacent sides are of the same length and the diagonals intersect at right angles.

         3.3.3 Parallelogram - A parallelogram is a closed, four sided two-dimensional figure whose opposite sides are equal in length and parallel to each other. The opposite angle can also be the same. It is useful to know the properties of the parallelogram to determine the sides and angles. 

        3.3.4 Elements of a Parallelogram - There are four sides and four angles in a parallelogram. Some of these are equal. It has some terms associated with these elements that you need to remember.

       3.3.5 Angles of a Parallelogram 

  • The two opposite sides of a parallelogram are the equal in size and parallel to each other.

  • Parallelograms can be viewed from opposite sides.

  • 360 degrees is the sum of all interior angles in a parallelogram.

  • Adjacent angles of Parallelograms are supplementary (180 degree).

        3.3.6 Diagonals of a Parallelogram - Parallelograms are derived from the Greek word which means “bounded by parallel lines”. Parallelograms are quadrilateral that have parallel lines on the opposite side. So, the sides of parallelograms are going to be equal and parallel. The diagonals are the line segments that intersect the opposite sides of the two vertices of a parallelogram.

3.4 Some Special Parallelograms 

           3.4.1 Rhombus - A rhombus is a kind of parallelogram that has two opposite sides that are parallel to each other and opposite angles are equal. The length of these sides is equal. The diagonals intersect at right angles.  A rhombus can also be called a diamond or rhombus diamond. Rhombi is the plural form for a rhombus.

          3.4.2 A Rectangle - A rectangle is defined as a quadrilateral whose sides are parallel to each other and all four vertices equal to 90 degrees. It is also referred to as the equiangular trilateral.It is also known as a parallelogram as the two sides of a rectangle are equal and parallel. A rectangle is a flat 2-dimensional shape. A rectangle can be represented by an XY plane.The length and width of the rectangle are indicated by the x-axis and y-axis arms respectively.

          3.4.3 A Square - A Square is a regular quadrilateral that has all sides having equal length. All four angles are equal. All the angles of a square are right angles or 90 degrees.The square's diagonals are also equal, and they intersect at a 90 degree angle. A rectangle is also called a square if its opposite sides are equal.

NCERT Solutions for Class 8 Maths Chapter 3 Exercises

NCERT Solutions for class 8 maths chapter 3 provides a detailed exercise-based analysis.

Exercise 3.1

2 Questions & Solutions

Exercise 3.2

6 Questions & Solutions 

Exercise 3.3

12 Questions & Solutions

Exercise 3.4

6 Questions & Solutions

Benefits of Downloading The NCERT Solutions for Class 8 Maths Chapter 3 - Understanding Quadrilaterals

The NCERT solutions for class 8 maths chapter 3 Understanding Quadrilaterals offers students the opportunity to gain a thorough comprehension of its properties. The following are some of the primary benefits of downloading and using these solutions:

  1. Every question and concept is described step by step in these solutions.

  2. NCERT solutions by eSaral provide clear definitions and concepts related to quadrilaterals, providing students with a solid conceptual basis to understand the topic in depth.

  3. NCERT solutions in chapter 3 of class 8 maths include Diagrams, Figures, and Illustrations to help students see the properties of quadrilaterals and how they relate to each other more clearly.

  4. These solutions provide clear explanations and effective problem-solving strategies, helping students make better use of their study time.

Frequently Asked Questions

Question 1. What are Quadrilaterals as per NCERT solutions for class 8 maths chapter 3 ?

Answer 1. A quadrilateral, according to the NCERT, is a plane with four sides (or edges) and four corners (or vertices). You'll usually find quadrilaterals in four-sided shapes like rectangles, squares, trapezoids, and kites, as well as irregular and uncharacterized shapes. 

Question 2. Why is chapter 3 of NCERT solutions so important in class 8 maths ?

Answer 2. The NCERT Solutions for class 8 maths chapter 3 questions are not only relevant to the exams, but also to the overall knowledge of Quadrilaterals. These questions have been solved by the best teachers in the subject according to the NCERT guidelines. Once the students answer the questions, they will be able to understand the topic more easily and better.



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