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Question

How many triangles are there in the figure given below?

This question was previously asked in
SSC CGL 2024 (Tier-I) Previous Year Paper (17-Sep-2024) (Shift 3)
The correct answer is

11

To find the total number of triangles in the given figure, we need to systematically count each triangle formed by different intersections and combinations of lines.

1. **Individual Triangles**: Start by counting the smallest triangles. Assume these are the ones formed without any overlapping parts:

  • There are 4 small individual triangles.

2. **Combined Triangles**: Look for triangles formed by combining these small triangles or using sections formed by line intersections:

  • If we combine two small triangles, we form a new, larger triangle. Count how many unique combinations are possible:
  • 3 triangles made by combining two small triangles.
  • Look for triangles formed by combining three small triangles:
  • 3 triangles made by combining three small triangles.

3. **Largest Triangle**: Finally, consider the largest triangle that encompasses the entire figure. This accounts for:

  • The single, largest triangle that uses the outermost lines.

Adding up all these possibilities gives:

Total triangles = 4 + 3 + 3 + 1 = 11

Thus, the total number of triangles in the figure is 11.

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Similar Questions

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

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

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

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


Important Questions from Counting Figures

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

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

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

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

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