How many triangles are present in the given figure?
Show Hint
- 12
- 16
- 20
- 24
The Correct Option is D
Solution and Explanation
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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