# NCERT Solutions Class 9 Maths Chapter 9

## NCERT Solutions For Class 9 Mathematics Chapter 9 – Areas Of Parallelograms And Triangles

Mathematics is a subject that is better taught through conceptual explanations and solved illustrations. You need to be clear about the application of formulas to get better marks in the school examinations.

In the NCERT solutions for Class 9 Mathematics Chapter 9, one can find the concepts and formulas required to measure the areas of two-dimensional quadrilaterals such as Parallelograms, Squares, etc. If you are looking for the best techniques to solve math problems or better conceptual clarity about the areas of different mathematical shapes, then you must refer to the content available on the Extramarks website for Class 9 Mathematics NCERT Solutions Chapter 9 – Areas of Parallelograms and Triangles.

You can easily access the best study material  on the Extramarks website, along with the most extensive collection of solved examples and NCERT-based questions regarding the Areas of Parallelograms and Triangles. The Extramarks website provides comprehensive knowledge about the concepts and formulas related to the Areas of Parallelograms and Triangles. It also provides the students with a step-by-step guide to  excelling intheir school examinations. One can take the most advantage of this opportunity to clear all their doubts and pending questions through the rich study material and notes provided by the online learning and educational platform  Extramarks for NCERT Solutions for Class 9 Mathematics Chapter 9.

If you want the latest updates regarding the CBSE examinations, you must regularly visit Extramarks website. One can easily access the various topic solutions for NCERT Solutions Class 11 NCERT, NCERT Solutions Class 9, NCERT Solutions Class 12, NCERT Solutions Class 10, etc., on the Extramarks website. You can build a solid academic career with the quality study material and solved questions provided by this online learning and educational platform.

## Key Topics Covered In the NCERT Solution For Class 9 Mathematics Chapter 9 – Areas Of Parallelograms And Triangles

Extramarks NCERT Solutions for Class 9 Mathematics, Chapter 9, has a detailed analysis of each concept and topic through solved illustrations. The key concepts and essential topics that will be elaborated upon within this chapter are areas of parallelograms, triangles, a median of triangles, and other miscellaneous formulas/topics. You must take this chapter very seriously, as some of the topics covered in this chapter are also part of the syllabus for major competitive examinations such as NEET and IIT-JEE in the future.

One must be well-versed in the basic level of understanding of the measurement of the total area of 2-dimensional figures to properly solve the mathematical problems based upon the formulas for calculating the area of 2-dimensional figures.

Introduction

Shapes That Have Same Parallels And Are On The Same Base As Each Other-

In this section, students must understand that the measurement of the area of the planar surface of a 2-dimensional figure is based upon the space enclosed by the edges of the mathematical shape/figure.

In this figure, four types of mathematical shapes are present on the same baseline, i.e., straight line AB, and are also in between the same parallel lines EF and AB. The shapes include two triangles in ABQ and BAP, one Parallelogram in the form of ABCD, and one rectangle in the form of ABEF.

Areas Between Common Parallel Lines And Parallelograms With A Common Base

For a parallelogram to be classified as having a joint base and parallels with another parallelogram, two conditions must be met:

1. They share a common baseline in the form of a straight line (like the line AB or BA in Figure B)
2. They share standard parallel lines on the same side of the 2-dimensional shape (like the parallel lines AB and ED in Figure B)

In this figure, the areas of the 2 parallelograms, which are ABCD and ABEF, will be equal in measurement due to their a standard baseline AB, as well as common parallel lines, AB and ED.

Area of Parallelogram ABCD = Area of Parallelogram ABEF

Students will find more illustrations about understanding the area of 2 parallelograms in our NCERT Solutions for Class 9 Mathematics Chapter 9. First, they need to register on our Extramarks website and then access all our class-wise NCERT solutions.

Area Of Triangles With A Common Base And Between Same Parallel Lines –

There are two conditions that must be met for a triangle to be classified as having a joint base and parallels with another triangle:

1. They share a common baseline in the form of a straight line (like the line DF or FD in Figure B)
2. They share standard parallel lines on the same side of the 2-dimensional shape (like the parallel lines AB and ED in Figure B)

In figure B, the areas of the two triangles, which are DFB and DFA, will be equal in measurement due to their standard baseline DF and standard parallel lines, AB and ED.

The concept of area of triangles with a common base is elaborated further with more examples in our NCERT Solutions for Class 9 Mathematics Chapter 9.

Essential Formulae And Theorems For Calculating The Area Of A Triangle

In Figure C, it must be observed that the ‘base’ and ‘height’ of a triangle have been illustrated clearly, and half of the product of the base and height of the triangle is equal to the measurement of the total enclosed area given the triangle.

½ x b x h = Area of a Triangle

Essential Formulae And Theorems For Calculating The Area Of A Triangle And A Triangle With A Common Base And Between Common Parallel Lines

In Figure D, the parallelogram ABCE is on the same baseline BC as the triangle in the form of BCD. Therefore, we must infer the direct proportion arising out of the areas of these two mathematical shapes, which can be calculated in the following manner –

Area of the Triangle BCD = ½ of the Area of Parallelogram ABCE

Below, we have given a few examples of advanced concepts. Students can get full access to examples and solve problems on this topic, if they visit the Extramarks website.

How To Measure The Medians And Centroid Of A Triangle

Median has been defined as a line segment extending from any of the corners of the triangle to the opposite side. In total, we must understand that a triangle has three central medians, and the crossing point or intersection point of these three medians is known as the Centroid. The median partitions the triangle into two equal and identical halves.

In Figure E, point O is the intersection point of the three medians of triangle ABC, and hence it is known as the Centroid of the triangle. The straight lines AE, CD, and BF are known as the medians of the triangle ABC

NCERT Solutions For Class 9 Mathematics Chapter 9 Exercise & Answer Solutions

Mathematics is tough, and students should refer to study resources such as Extramarks NCERT Solutions for understanding the important topics that come up in the CBSE examinations. They can increase their problem-solving skills and memory through the study material available on the Extramarks website.

The various topics covered in this chapter include areas of parallelograms, triangles, medians of triangles, etc. With the suitable study material on the Extramarks website, you can quickly excel in your CBSE school examinations. The NCERT Solutions for Class 9 Mathematics Chapter 9 provide step-by-step guides and illustrations to increase the grasping power of students. Extramarks is one of the most reliable online learning platforms.

The NCERT Solutions for Class 9 Mathematics Chapter 9 are available on the Extramarks website for your reference. It uses examples and conceptual illustrations to clarify the topics in the students’ minds in a step-by-step manner. You can quickly grasp the formulas and concepts of measuring the areas of parallelograms and triangles through the NCERT Solutions available on our website..

The exercise and solutions in the NCERT Solutions for Class 9 Mathematics Chapter 9 – Areas of Parallelograms and Triangles can be accessed by clicking on the link as given below –

• Chapter 9 – Exercise 9.1 – Short Answer Type Questions – Total 6 Questions
• Chapter 9 – Exercise 9.2 – Very Short Answer Type Questions – Total 10 Questions
• Chapter 9 – Exercise 9.3 – Long Answer Type Questions – Total 16 Questions
• Chapter 9 – Exercise 9.4 – Optional Type Questions – Total 8 Questions

Along with the detailed analysis of NCERT Solutions for Class 9 Maths Chapter 9 NCERT solutions, you can also explore the study material for –

• NCERT Solutions Class 1
• NCERT Solutions Class 2
• NCERT Solutions Class 3
• NCERT Solutions Class 4
• NCERT Solutions Class 5
• NCERT Solutions Class 6
• NCERT Solutions Class 7
• NCERT Solutions Class 8

NCERT Exemplar Class 9 Mathematics Chapter 9 – Areas of Parallelograms and Triangles

The exemplar consists of a detailed answer key and solved illustrations to help the students revise their formulas and concepts appropriately before the exam. The Extramarks online learning platform enables students to comprehend mathematical concepts by providing comprehensive study materials such as NCERT Solutions for Class 9 Mathematics Chapter 9.

The Exemplar provides the students with a large number of questions as well as notes to properly prepare for their final examinations in school. The solved questions of the NCERT Exemplar for Class 9 Mathematics Chapter 9 are available on the Extramarks website.

Once students are well-versed in the concepts, they can easily compete in the major competitive examinations such as NEET, IIT-JEE, WBJEE, etc. which can help them enter some of the most prestigious universities in our country in the future. You can also access the study material regarding NCERT Solutions Class 10, NCERT Solutions Class 11, NCERT Solutions Class 12, etc. on the Extramarks website.

Key Features Of NCERT Solutions For Class 9 Mathematics Chapter 9

The NCERT Solutions for Class 9 Mathematics Chapter 9 allow the students to revise their core concepts and essential formulas right before the exam day. A concise and well-illustrated set of notes helps them achieve maximum marks in their school examinations. The key features and essential concepts of the NCERT Solutions for Class 9 Mathematics Chapter 9 are provided as follows –

• On the Extramarks learning platform, only qualified experts and renowned academicians create the study material for NCERT Solutions of Class 9 Mathematics Chapter 9 – Areas of Parallelograms and Triangles.
• The NCERT Solutions helps in revising the fundamental concepts and formulas in the future. Then, in a step-by-step manner, they can also grasp the more complex and advanced topics covered under the CBSE syllabus and IIT-JEE preparation guide.
• By understanding the concepts and formulas relating to the areas of Parallelograms and Triangles, the students can solve many higher-level mathematical problems and architectural engineering problems.