While counting triangles, always count systematically: start with the smallest triangles, then medium ones, and finally the largest shapes to avoid missing any.
Step 1: Understanding the figure.
The figure consists of a rectangular shape on the right side and a triangular extension on the left side. Several diagonals and horizontal and vertical lines divide the figure into smaller regions. These lines create multiple overlapping triangles of different sizes and orientations. Step 2: Counting small triangles.
First, we count all the smallest individual triangles formed by the intersecting lines. By carefully observing each small triangular region inside the figure, we find a total of 8 small triangles. Step 3: Counting medium-sized triangles.
Next, we count triangles formed by combining two or more small triangles. These include triangles formed by diagonals inside the rectangle and the triangular extension. There are 5 medium-sized triangles. Step 4: Counting large triangles.
Finally, we count the largest possible triangles formed by the outer boundaries of the figure and major diagonals. There are 2 large triangles. Step 5: Final calculation.
Total number of triangles = Small triangles + Medium triangles + Large triangles
\[
8 + 5 + 2 = 15
\] Step 6: Conclusion.
Hence, the total number of triangles present in the given figure is 15.
