Question

How many triangles are there in the following figure? 

• A. 16
• B. 14
• C. 8
• D. 12

Hint:

When counting shapes, always proceed from smallest to largest and ensure no overlaps are counted twice.

Answer 1

The Correct Option is A

Step 1: The figure is a rectangle divided into multiple parts with diagonals and medians.
Step 2: We count triangles systematically:
- Small triangles formed directly by the intersection lines: There are 8 small triangles.
- Larger triangles formed by combining two small ones: There are 4 such triangles.
- Even larger triangles formed by combining four small ones: There are 4 such triangles.
Step 3: Add them all:
\[ 8 \ (\textsmall) + 4 \ (\textmedium) + 4 \ (\textlarge) = 16 \] Step 4: There is no triangle double-counted because each set counted is distinct by size and position.
Thus, the figure contains exactly $\mathbf16$ triangles.