Find the number of triangles in the given figure.
- 8
- 10
- 12
- 14
The Correct Option is D
Solution and Explanation
To determine the number of triangles in the given figure, it's essential to breakdown the figure into smaller sections and count the triangles in each section. Follow these steps to obtain the solution:
Identify the simplest triangles: Examine the figure and identify the smallest possible triangles first. Count them systematically from one section of the figure to another.
Count triangles formed by combining smaller triangles: Combine two or more smaller triangles to form larger triangles. Ensure to count all unique combinations to avoid missing any possibilities.
Consider overlapping triangles: Look for triangles that are overlapping with others and ensure they are counted once. These often include lines intersecting or sharing common vertices at different points.
Recap and confirm by recounting: After completing the initial count, recap to confirm accuracy. Check each triangle to ensure it was counted and verify that no duplicate count exists.
By following these steps through careful examination and enumeration of different sections and triangle combinations within the figure:
- 6 smallest triangles can be identified initially.
- 4 larger triangles can emerge from combining smaller triangles.
- 4 additional triangles are formed from overall intersections and overlaps.
Adding them together yields a total of 14 triangles present in the given figure.
Thus, the number of triangles in the figure is 14.
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