How many triangles are there in the given figure?
11
This is a counting-figures problem, so the reliable method is to count the triangles in a fixed order rather than at random, which prevents both missing a shape and counting one twice.
The first pass counts the smallest, indivisible triangles formed directly by the intersecting lines of the figure.
The next pass counts the larger triangles built by joining two or more of these smallest pieces along their shared edges.
Summing the simple triangles and the composite triangles gives the complete tally, with each triangle counted once and only once.
Carrying out this ordered count over all three-sided regions yields eleven triangles in total; the figure itself is not reproduced here.
Hence the number of triangles in the figure is 11.
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