NCERT Solutions for Class 9 Maths Exercise 9.4 Areas of Parallelograms and Triangles

Before proceeding to solve the questions numbering 8 in this exercise 9.4 we should be able to recollect all the important properties that we have previously learnt in chapter 9. Some of the important property have been highlighted to make the exercise student-friendly.

1. Parallelograms having same base (for example 6 cm each) and between the same parallels have equal area.
2. Area of a parallelogram is arrived that by multiplying the base with the corresponding altitude. For example, if the base of parallelogram is 6 cm and altitude is 5 cm, its area will be 30 square cm.

Theorems play an important role in solving the questions particularly in geometry. One of the important theorems of class 9 Maths exercise 9.4 are states If a parallelogram and a triangle are having the same base and a lie between the same parallel lines then the area of such a triangle shall be half of the area of such a parallelogram. This is a very important property.

The following theorems are required to keep in mind, if we are trying to solve the questions given in Exercise 9.4 of class 9 mathematics. The first theorem – Area of any triangle is one half of the product of its base and the corresponding altitude.

The second is triangle on the same base and same parallel lines have equal area. Similarly there is one more to apply most of the questions. A Median of a triangle divides the triangle into two parts having equal areas. Of course we should recollect the important property of medians that they are concurrent (meet and the same point) it is called the centroid.

We are suggesting certain important question for practise. Question number 2, 4, 5, 6, and 7 particular question 8. Question number 8 is nothing but the prof of the famous Pythagoras theorem. In fact, the Pythagoras theorem has several profs. A simple prof has been provided to students of higher classes. This shows the versatility of geometry—as an important branch of mathematics.

In other words, the same thing can be proved by different ways or by applying different methods. We advise students to workout exercise 9.4 particularly because it will help to review the entire chapter 9. Further, the number of question is just 8, so it is not time consuming.