Question

Find the number of triangles from the figure. 

• A. 20
• B. 24
• C. 28
• D. 29
• E. 32

Hint:

For figures where a square is divided by both diagonals, use the formula $n \times 2$, where $n$ is the number of small internal triangles. In this figure, the main square has 4 small parts, so $4 \times 2 = 8$. Apply this systematically to each section and then look for the large "hidden" triangles that span across multiple sections.

Answer 1

The Correct Option is C

Concept: To find the total number of triangles in a complex geometric figure, it is best to break the image down into its fundamental components (small squares/quadrants) and then count larger triangles formed by merging those components.

Step 1: Counting triangles in the central square.
The central square is divided by two diagonals into 4 small triangles. Small triangles: 4 Triangles formed by 2 small triangles: 4 (Each side of the square serves as a base) Sub-total for center: $4 + 4 = 8$ triangles.


Step 2: Counting triangles in the corner squares.
There are 4 small squares attached to the corners of the main grid. Each corner square is divided by one diagonal. Triangles per corner: 2 Total for 4 corners: $2 \times 4 = 8$ triangles.


Step 3: Counting triangles formed by larger grid sections.
The larger internal $2 \times 2$ grid (excluding the outermost corner attachments) is also bisected by the main long diagonals. Large triangles (using the full main diagonals): 4 Medium triangles (within the quadrants): 8


Step 4: Summing the totals.
Total count = (Center 8) + (Corners 8) + (Large Diagonals 4) + (Internal grid overlaps 8) = 28 triangles.