Question

Find the number of triangles in the following figure:

• A. 16
• B. 17
• C. 19
• D. 21

Answer 1

The Correct Option is D

To determine the number of triangles in the given figure, follow these steps:

1. Identify Small Triangles: Count the smallest triangles formed by the intersections. This figure has 8 smallest triangles.
2. Combine Small Triangles to Form Larger Ones:
   • Combine two small triangles to form larger triangles. There are 6 such combinations.
3. Combination of Three or More Triangles: Check for combinations leading to larger triangles:
   • Three triangles can form another 4 larger triangles.
4. Count Overlapping and Cross-Triangle Configurations:
   • Crossing lines create unique triangles. There are 3 such configurations.
5. Total Count of Triangles: Add all the triangles from the above steps:
   8 + 6 + 4 + 3 = 21

Thus, the total number of triangles in the given figure is 21.