Question

Find the number of triangles in the following figure: 

• A. 27
• B. 25
• C. 23
• D. 21
• E. 29

Hint:

For complex figures, label the vertices or the individual "rooms" (small areas) with numbers or letters. List the triangles by their components (e.g., Triangle 1, Triangle 1-2, Triangle 1-2-5-6) to avoid double-counting.

Answer 1

The Correct Option is B

Concept:Counting triangles in complex geometric figures requires a systematic approach to ensure no overlaps or omissions. We categorize triangles by their size (single units, combinations of 2 units, 3 units, etc.) or by identifying symmetrical sub-structures within the main figure.
Deconstructing the figure:
The figure consists of a large inverted triangle and a smaller upright triangle intersecting it, with several internal divisions creating smaller geometric regions.
• Smallest individual triangles: Counting the basic, non-overlapping triangles formed by the intersections results in 16 small triangles.
• Medium-sized triangles (formed by 4 units): By combining 4 smaller units, we can identify 7 medium triangles (some pointing up, some pointing down).
• Large triangles (formed by multiple units): There are 2 large primary triangles that form the outer boundary of the star-like intersection. Summing these categories: $16 + 7 + 2 = 25$.