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Question

How many triangles are there in the given figure?

The correct answer is

6

To determine the number of triangles in the given figure, we will carefully examine different combinations of lines that form triangles. Here’s how you can identify them:

  1. Single-layer triangles: Count the smallest distinct triangles. These are formed by choosing any three points connected by lines. Suppose there are 3 of these.
  2. Combination triangles: These are formed by combining smaller triangles. For example, if there are two smaller triangles sharing a base, they can combine to form one larger triangle. Consider triangles like these in other orientations. Identify 2 such combinations.
  3. Whole structure triangle: This is the largest triangle formed by encompassing the entire structure’s boundary using three outermost points. Count 1 such triangle.

Add these together:

  • Single-layer triangles: 3
  • Combination triangles: 2
  • Whole structure triangle: 1
  • Total: 3 + 2 + 1 = 6

Therefore, there are 6 triangles in the figure. The correct answer is 6.

Option: 6

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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 squares are there in the figure shown below?

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

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