Question:
In the figure given above there are maximum ........... number of triangles that can be identified
(Note:- DO NOT include spaces in your answer)
In the figure given above there are maximum ........... number of triangles that can be identified
(Note:- DO NOT include spaces in your answer)
Updated On: Jul 16, 2026
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Correct Answer: 12
Approach Solution - 1
In the given figure, the explanation outlines the maximum number of triangles that can be identified. It lists various combinations of three vertices that form triangles within the figure, summing up to a total of 12 triangles. Each triangle is derived from connecting three non-collinear points within the figure's layout.12 triangles are possible.
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Approach Solution -2
Rather than listing triangles one at a time from memory, count them by size category, which is the reliable way to make sure none are missed or repeated.
- Smallest (single-cell) triangles: identify every triangle formed directly by three lines meeting at their nearest intersection points, without any other line crossing through it.
- Medium (two-cell) triangles: identify every triangle formed by combining two of the smallest triangles that share a common side, checking that the outer boundary is still a straight-sided triangle and not a different shape.
- Largest (whole-figure) triangles: identify every triangle formed by the outermost lines of the figure, which encloses all the smaller triangles inside it.
- Add up each category: summing the smallest, medium and largest triangles found in the figure gives the maximum count without double-counting or missing any combination.
Working through the figure category by category in this way gives a total of 12 distinct triangles.
Therefore, the maximum number of triangles that can be identified is 12.
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