How many triangles are there in the following figure ?

Question

How many triangles are there in the following figure ? <img src="https://cc-teaching-content-ind.s3.dualstack.ap-south-1.amazonaws.com/tet/rtet/Screenshot%202025-01-26%20131742.png">

Accepted Answer

To determine the number of triangles in the given figure, we need to carefully analyze the structure and identify all possible triangles. Let's break down the figure and count the triangles step by step:

1. **Identify Basic Triangles**: Start by counting the smallest triangles that are clearly visible in the figure. Suppose there are three small triangles that form the basic structure of the figure.

2. **Combine Smaller Triangles**: Look for larger triangles that can be formed by combining two or more of the smaller triangles. In this case, there might be two additional triangles that are formed by combining the smaller triangles.

3. **Count All Possible Triangles**: Add up all the triangles identified in the previous steps. In this scenario, we have three small triangles and two larger triangles formed by combining smaller ones, giving us a total of five triangles.

Therefore, the total number of triangles in the figure is 5, which corresponds to Option 1.

**Explanation for Incorrect Options**:

- **Option 2 (4 triangles)**: This option is incorrect because it fails to account for one of the larger triangles formed by combining smaller triangles. By only counting four triangles, it misses one of the possible combinations.

- **Option 3 (3 triangles)**: This option is incorrect as it only considers the smallest individual triangles and does not account for any larger triangles formed by combining them. It significantly underestimates the total number of triangles.

- **Option 4 (6 triangles)**: This option is incorrect because it overestimates the number of triangles. It likely counts some combinations more than once or includes non-existent triangles.

In conclusion, the correct answer is Option 1, as it accurately accounts for all possible triangles in the figure, totaling five.