Theory:

In this session, we shall learn that the triangles on the same base and between the same parallels are equal in the area using an activity.
 
Activity:
 
Consider drawing triangles \(ABC\) and \(DBC\) in a graph sheet having the same base and between the same parallels.
 
11.png
 
The above figure shows that the triangles are on the same base \(BC\) and between the same parallels \(l\) and \(BC\).
 
In grade \(6\), we have learnt how to find the area by counting the number of squares in the graph.
 
Now, applying this concept, let us find the area of the triangle \(ABC\) and \(DBC\).
 
Consider the triangle \(ABC\).
 
12.png
 
Area of fully-filed squares \(= 3 \times 1 = 3 \ sq. \ cm\).
 
Area of half-filled squares \(= 3 \times \frac{1}{2} = 1.5 \ sq. \ cm\).
 
Area of more than half-filled squares \(= 0\)
 
Area of less than half-filled squares \(= 0\)
 
Therefore, the area of the triangle \(ABC\) is \(3 + 1.5 = 4.5 \ sq. \ cm\).
 
Similarly, consider the triangle \(DBC\).
 
13.png
 
Area of fully-filed squares \(= 3 \times 1 = 3 \ sq. \ cm\).
 
Area of half-filled squares \(= 3 \times \frac{1}{2} = 1.5 \ sq. \ cm\).
 
Area of more than half-filled squares \(= 0\)
 
Area of less than half-filled squares \(= 0\)
 
Therefore, the area of the triangle \(ABC\) is \(3 + 1.5 = 4.5 \ sq. \ cm\).
 
Since the areas of both the triangles \(ABC\) and \(DBC\) are the same, we conclude that "triangles on the same base and between the same parallels have equal areas".