Question

Count the member of triangles in the following figure.

• A. 8
• B. 12
• C. 9
• D. 14

Answer 1

The Correct Option is B

To determine the number of triangles in the given figure, we need to carefully analyze how the lines intersect to form different triangles. Let's count step-by-step:

1. Identify the simplest triangles that are visible. These are the smallest divisions resulting from the intersecting lines. Let's count them:
   • There are 8 small triangles at the outer corners. These are formed at each of the four points where the diagonal lines intersect the outer square.
2. Count the triangles that are formed by combining two of the small triangles:
   • There are 4 such triangles, each formed by combining two adjacent small triangles along the lines that bisect the square horizontally and vertically.
3. Finally, observe the larger triangles formed by the intersection of diagonals:
   • There are 4 such triangles, each formed by considering the sections divided by the intersecting lines passing through the center.

Adding these up, we have a total of \(8 + 4 + 4 = 12\) triangles.

Based on the above counting, the correct answer is 12.