Question

Find the number of triangles in the given figure.

• A. \(10\)
• B. \(12\)
• C. \(14\)
• D. \(16\)
• E. \(18\)

Answer 1

The Correct Option is C

Concept: This is a
counting triangles problem involving:

• Identifying smallest triangles
• Combining smaller triangles to form larger ones
• Avoiding repetition while counting

Step 1: Count smallest triangles.
Carefully observe and count all basic unit triangles in the figure: \[ \text{Number of smallest triangles} = 8 \]
Step 2: Count medium-sized triangles.
Combine adjacent small triangles: \[ \text{Number of medium triangles} = 4 \]
Step 3: Count largest triangles.
Formed by combining multiple sections: \[ \text{Number of large triangles} = 2 \]
Step 4: Total triangles.
\[ 8 + 4 + 2 = 14 \]
Step 5: Option analysis.

• (A) 10: Missing several combinations $\times$
• (B) 12: Incomplete counting $\times$
• (C) 14: Correct total \checkmark
• (D) 16: Overcounting $\times$
• (E) 18: Excess counting $\times$

Conclusion:
Thus, the correct answer is
Option (C).