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Question

Find the number of triangles in the figure given below: 

This question was previously asked in
RRB NTPC 2019 CBT 1 Question Paper (8-Mar-2021) (Shift 2)
The correct answer is
44 triangles

To determine the total number of triangles in the given figure, we need to analyze and count the triangles systematically by inspecting various parts and combinations within the structure.

Let's break it down:

  1. There are four large equilateral inner triangles, each made by dividing the central rectangle. These are the most visible triangles.
  2. Within each of these large equilateral triangles, there are smaller triangles formed. Each large triangle contains 3 smaller triangles (1 downward, 2 upward).
  3. This results in \(4 \times 3 = 12\) smaller triangles within the larger triangles.
  4. The central rectangle itself is split into smaller triangles through diagonal and vertical lines.
  5. Above and below the central rectangle, triangle formations consist of large triangles enclosing smaller ones. Each side accounts for 10 triangles:
    • 2 triangles by the vertical division (left and right segments).
    • 6 medium triangles in total (3 on each side).
    • 2 small triangles, distinctive above and below the rectangle.
  6. Adding 10 triangles for both upper and lower sections gives us \(10 \times 2 = 20\) triangles.
  7. Finally, there are additional triangles formed by combining smaller triangles across the structure:
    • The top and bottom apex structures contribute 5 triangles each in the larger formation.
  8. Add all triangles: \(12\) (from inner large triangles) \(+\) \(20\) (from upper and lower sections) \(+\) \(12\) (6 and 6 from top and bottom)
  9. This gives a total of \(44\) triangles.

Therefore, the correct answer is 44 triangles.

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Similar Questions

  1. Find the total number of triangles in the following figure.

  2. How many triangles does this figure have?

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

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

  5. How many pentagons are there in the given figure?

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

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  9. What is the minimum number of straight lines in the following figure?

  10. Find the minimum number of straight lines in the following figure.


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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