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Question

Find the number of triangles in the given figure.

The correct answer is
48

To determine the total number of triangles in the given figure, we need to carefully analyze the structure and count all possible triangles of different sizes.

Step-by-step Counting:

  1. Begin by counting all the small triangles formed directly by the intersecting lines within the figure.
  2. Next, identify the medium-sized triangles, which are formed by combining two or more of the smaller triangles.
  3. Consider all larger triangles, made up of combinations of smaller and medium triangles, including those that extend to cover larger sections of the diagram.

By careful combinatorial counting, the triangles can be classified and counted methodically:

  • Small triangles: 24
  • Medium triangles: 16
  • Large triangles: 8

Adding these, we get the total number of triangles:

24 + 16 + 8 = 48

Hence, the total number of triangles in the figure is 48.

Conclusion: The correct option is 48.

This method ensures that all possible combinations are considered, avoiding duplication and omission.

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Important Questions from Counting Figure (Notes)

  1. Find the number of triangles in the given figure

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

  3. In the following question, select the figure which can be placed at the sign of question mark (?) from the given alternatives.

  4. In the following question, select the figure which can be placed at the sign of question mark (?) from the given alternatives.

  5. Find the number of triangles in the given figure.

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