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Question

How many triangles are there in the given figure.

The correct answer is
14

To determine the number of triangles in the given figure, we need to systematically count all possible triangles, including smaller and larger ones. Let's analyze the figure step-by-step:

  1. Triangular Sections: Look at each section of the figure independently. There are several triangular regions formed by the intersecting lines both horizontally and vertically.
  2. Smaller triangles: Count the smaller triangles within each section.
    • The leftmost section has small triangles formed by lines converging at a point. There are 4 small triangles here.
    • The top-right section has 4 small triangles.
    • The bottom-right section also has 4 small triangles.
  3. Larger triangles: Combine smaller triangles to form larger ones.
    • In the entire figure, combining triangles from different sections, there are 2 larger triangles in each right section.
    • Lastly, observe any triangles formed by aggregating smaller triangles across sections. There are 2 such triangles.
  4. Total Count: Adding these together:
    • 4 (left section) + 4 (top-right) + 4 (bottom-right) + 2 (combined larger) = 14 triangles.

Conclusion: The total number of triangles in the figure is 14. Therefore, the correct answer is 14.

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Important Questions from Figure Counting

  1. How many triangles are there in the given figure?

  2. How many squares are there in the given figure?

  3. How many squares are there in the figure shown below?

  4. How many triangles are there in the given figure?

  5. How many squares are there in the figure shown below?

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