Question

Find the number of triangles in the given figure.

• A. \(10\)
• B. \(11\)
• C. \(12\)
• D. \(14\)
• E. \(16\)

Answer 1

The Correct Option is D

Concept: This is a
counting triangles problem involving:

• Identifying smallest triangles
• Forming larger triangles by combining smaller regions
• Ignoring curved boundaries (only straight-line triangles count)

Step 1: Ignore curved parts.
The circular portion does not form triangles since it contains curved edges. Only straight-line regions are considered.
Step 2: Count smallest triangles.
Carefully observe the central and right structure: \[ \text{Small triangles} = 8 \]
Step 3: Count medium triangles.
Formed by combining adjacent smaller triangles: \[ \text{Medium triangles} = 4 \]
Step 4: Count larger triangles.
Formed using bigger sections: \[ \text{Large triangles} = 2 \]
Step 5: Total triangles.
\[ 8 + 4 + 2 = 14 \]
Step 6: Option analysis.

• (A) 10: Under-counted (misses combinations) $\times$
• (B) 11: Incomplete count $\times$
• (C) 12: Missing larger triangles $\times$
• (D) 14: Correct count \checkmark
• (E) 16: Over-counted $\times$

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