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How many triangles does the figure contain ?

Solution

The classic “how many triangles” puzzle challenges you to count all possible triangles in a given figure — not just the small ones, but also combinations that form larger ones.
Counting triangles is a common reasoning exercise in math, often used in contests and interviews, and helps develop spatial visualization and combinatorial thinking.
In the next section, we will carefully identify and count each triangle one by one to reach the final total.

To find how many single triangle we have in the figure, let’s take out each one separately.
So, the biggest one is the first triangle
Next, two triangles
Two other triangles
Finally, one triangle
Therefore, the figure contains 6 triangles.

After listing each triangle separately — the largest one, the medium ones, and the smaller ones — we verified that the figure contains a total of 6 triangles, as shown in the official solution.
This problem is a great example of how systematic decomposition (counting one shape at a time) can simplify what looks like a complex puzzle.
For more similar shape‑counting puzzles, visit our Solved Exercises section.

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How many triangles does the figure contain ?
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