NCERT Solutions for Class 9 Maths Chapter 9 Areas Of Parallelograms And Triangles: Understanding the area of triangles and parallelogram is mandatory in the field of calculating the area of land. If a land has an irregular shape the land will be divided into triangles and area will be calculated. And also many other structures have the shape of the triangle and parallelograms. NCERT Solutions for Class 9 Maths Chapter 9 Areas Of Parallelograms And Triangles introduces the concepts of area of triangle and parallelogram and their properties. There are several interesting problems in the chapter. Solving these problems will help you in improving the concepts of the chapter and also in exams like olympiad. The main topics of NCERT Solutions for Class 9 Maths Chapter 9 are listed here.
9.1 Introduction
9.2 Figures on the Same Base and Between the Same Parallels
9.3 Parallelograms on the same Base and Between the Same Parallels
9.4 Triangles on the same base and between the same Parallels
The main theorems mentioned of NCERT Solutions for Class 9 Maths Chapter 9 are listed below:
1. Parallelograms on the same base and between same parallels are equal in the area
Figure 1
That is in figure 1 the parallelograms ABCD and EFCD have the same base CD and lies between same parallels AF and CD. Therefore area(ABCD)=area(EFCD).
2. Parallelograms on the same base (or equal bases) and having equal areas lie between the same parallels. This is the converse of the above property
3. Triangles on the same base (or equal bases) and between the same parallels are equal in area. That is in figure 2 the triangles ABC and BCD lie on the same base BC and Parallels BC and AD. Therefore by Theorem 3 area(triangle ABC) = area(tringle BCD)
4. The converse of property 3 is also true. That is two triangles having the same base (or equal bases) and equal areas lie between the same parallels.
Certain points to remember from this chapter of NCERT Solutions for Class 9 Maths are listed below:
i) Two congruent figures have equal area but two figures with the equal area may not be congruent. For example, a circle and a triangle having equal area are not congruent.
ii) If a parallelogram and a triangle lie on the same base and between the same parallels, then the area of the triangle= 0.5( the area of the parallelogram)
iii) Median of a triangle divides it into two triangles with equal area
There are four exercises mentioned in the NCERT Solutions of this chapter. Solving all the questions of NCERT Solutions for Class 9 will give a better understanding of the concept and will help in exams also.
The detailed NCERT Solutions for Class 9 Maths Chapter 9 Areas Of Parallelograms And Triangles are given below.
Chapter No. 
Chapter Name 
Chapter 1 

Chapter 2 

Chapter 3 

Chapter 4 

Chapter 5 

Chapter 6 

Chapter 7 

Chapter 8 

Chapter 9 

Chapter 10 

Chapter 11 

Chapter 12 

Chapter 13 

Chapter 14 

Chapter 15 
NCERT Solutions for Class 9 Maths 
NCERT Solutions for Class 9 Science 
Q: 6
A farmer was having a field in the form of a parallelogram PQRS. She took any point A on RS and joined it to points P and Q. In how many parts the fields is divided? What are the shapes of these parts? The farmer wants to sow wheat and pulses in equal portions of the field separately. How should she do it?
Q : 14 In Fig. , . Prove that .
Q: 5 In Fig. , ABC and BDE are two equilateral triangles such that D is the midpoint of BC. If AE intersects BC at F, show that
(ii)
[Hint: Join EC and AD. Show that and , etc.]