How many triangles are present in the given figure?
Show Hint
When solving triangle-counting problems, always count in layers: first the smallest units, then combinations of two, then larger ones. This prevents missing hidden triangles.
Step 1: Observe the figure.
The figure is a large quadrilateral (a slanted parallelogram-like shape) divided by several lines:
- Two vertical slanting lines divide it into three main sections.
- Two diagonal slanting lines across each section further subdivide the shape.
Step 2: Count small triangles.
Each smaller region formed by the internal lines can be broken into triangles. Carefully counting the simplest (smallest) triangles across all regions gives 12 small triangles.
Step 3: Count larger triangles.
By combining two or more small triangles, larger triangles are also formed:
- Triangles formed by combining two adjacent small ones = 8.
- Triangles formed by combining three or more adjacent ones = 4.
Step 4: Total count.
Adding them together:
\[
12 + 8 + 4 = 24
\]
Final Answer:
\[
\boxed{24}
\]
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