NCERT Solutions for Class 9 Maths Exercise 9.1 Areas of Parallelograms and Triangles

In chapter 5, we had studied about the concept of Euclid Geometry which is the basis of the entire subject of geometry. Now we shall proceed to the next step-that is, the study of parallelograms and triangles. The first two exercises are devoted to study of and practice of question relating to parallelograms and there are not many questions in these exercises but require application of mind. In fact, class 9 exercise 9.1 contains a very simple question regarding identification of the common base and two parallels from the figures given.

There are some activities to perform as well to understand theorem 9.1 which says that parallelograms between the same base and between the same parallels are equal in area. It is to be noted that a rectangle and a square are also parallelograms having special properties. In real life situations we come across certain situations where we have to measure the area of parallelograms. For example, in certain villages and towns, the plots are designed in a shape which is more or less like a parallelogram.

So until we know how to measure the area of parallelogram, business transactions relation to purchase and sale, imposition of property tax will become difficult. No wonder that along with the students the statutory authorities like the officers of property tax department in every state should know the formulae for calculating the areas of various geometrical figures. These figures may be triangle, parallelogram, trapezium and others. The lack of such knowledge will make their task difficult.

The most important property which is used is that parallelograms between the same parallels and same ways have equal area. The formulae for calculating area for parallelogram is the product of the base of the parallelogram and its corresponding altitude. It can also be said that of parallelograms have same base and equal area then they must for lie between the same parallels.