Question

The number of triangles in the given figure is:

• A. \( 8 \)
• B. \( 10 \)
• C. \( 12 \)
• D. \( 14 \)

Hint:

Systematically count triangles by size, starting with the smallest. Be careful not to double-count or miss any. Look for combinations of basic shapes that form larger triangles.

Answer 1

The Correct Option is C

Step 1: Identify the smallest triangles.
There are 8 small triangles formed by the intersecting lines within the central quadrilateral. Step 2: Identify triangles formed by combining two small triangles.
There are 4 triangles formed by combining two adjacent small triangles, using the diagonals of the four smaller squares formed. Step 3: Total count.
Total number of triangles = Number of smallest triangles + Number of triangles formed by combining two smallest triangles Total = \( 8 + 4 = 12 \)