How many triangles are there in the given figure?
12
The figure is a large right-angled triangle inside which several cevians (slanting lines) are drawn from the top and base, dividing it into many smaller triangular regions.
To avoid mistakes, count layer by layer: smallest single triangles first, then triangles built from two or three of those parts, and finally the whole outer triangle.
Smallest triangles: each individual triangular cell created where the lines cross gives 7 basic triangles.
Two-part triangles: pairs of adjacent small triangles sharing a common side combine to form 3 more triangles.
Larger triangles: bigger combinations of three regions form 1 more triangle.
The complete outer right triangle itself is the last one, adding 1 more.
Total \(= 7 + 3 + 1 + 1 = 12\), with no triangle repeated or missed.
Hence the figure contains 12 triangles.
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