How many triangles are there in the given figure?
2016
How many triangles are there in the given figure?

- A.
23 or more
- B.
20
- C.
16
- D.
12
Attempted by 5 students.
Show answer & explanation
Correct answer: A
1. Count the smallest, individual triangular regions first: There are 5 in the top rectangular section, 5 in the middle section, and 2 in the bottom pointed tip, giving 12 basic triangles. 2. Next, look for triangles formed by combining 2 or more smaller regions. The entire bottom tip forms 1 large triangle. 3. Trace the longer continuous straight lines to find large overlapping triangles. For example, the diagonals create 4 large triangles spanning across the middle horizontal line, and 4 large right-angled triangles in the outer corners of the rectangular portion. 4. Adding the 12 base triangles to the numerous larger combined geometric shapes (12 + 1 + 4 + 4 + ...) quickly pushes the total count to 23 or more. Final Answer: Option A