Question

Find the number of triangles in the given figure:

• A. 16
• B. 13
• C. 12
• D. 15
• E. 14

Hint:

Use a pencil to trace or a system of labeling points (like A, B, (c) to ensure you count every unique triangle only once.

Answer 1

Answer: (E)

Step 1: Understanding the Concept:
To find the total number of triangles, we must count all simple triangles and all triangles formed by combining smaller regions.
Step 2: Key Formula or Approach:
Systematically count by size: triangles made of 1 part, 2 parts, 3 parts, and so on.
Step 3: Detailed Explanation:
1. Smallest individual triangles: Counting the distinct smallest regions that are triangles yields 8 triangles in the central hub.
2. Medium triangles (made of 2 regions): Combining adjacent pairs of small triangles forms 4 larger triangles.
3. Largest triangles (made of multiple regions): Combining wider sections of the outer frame and inner regions reveals 2 more distinct triangles.
Total = \( 8 + 4 + 2 = 14 \).
Step 4: Final Answer:
The total number of triangles is 14.