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.

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 $$ABC$$.

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 $$DBC$$.

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".