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Count the triangles within the inner diamond (4 small, 4 combined = 8) and then look for additional triangles formed by the external lines (4 large ones).
Count the triangles within the inner diamond (4 small, 4 combined = 8) and then look for additional triangles formed by the external lines (4 large ones).
Analyze the inner diamond
The central diamond shape is divided into 4 small triangles. By combining adjacent small triangles, we get 4 additional triangles (top-bottom pair and left-right pair). This gives a total of 8 triangles within the inner diamond structure.
Analyze external triangle formations
The vertical lines intersect the diamond's vertices. The large triangles are formed by the central horizontal line and the outer vertical boundaries: 2 large triangles pointing upwards and 2 large triangles pointing downwards, totaling 4 additional triangles.
Sum the total
Adding the inner 8 triangles to the 4 large external triangles results in a total of 8 + 4 = 12 triangles.
A: 14 is incorrect because it overcounts the intersecting regions; C: 18 is incorrect as it assumes non-existent overlaps; D: 16 is incorrect because it fails to exclude shapes that are not closed triangles.
B is correct because the figure consists of 8 internal diamond-based triangles and 4 larger external triangles, summing to exactly 12.
When counting triangles in complex grid-based figures, always count the smallest individual units first, then systematically combine them into larger polygons to avoid double-counting.
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