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Systematically count individual triangles first, then identify composite triangles by combining adjacent sections, ensuring no overlapping shapes are missed.
Systematically count individual triangles first, then identify composite triangles by combining adjacent sections, ensuring no overlapping shapes are missed.
Categorize Single Triangles
Identify the smallest triangles: there is 1 triangle in the top-left corner, 1 triangle in the top-right of the left-vertical quadrant, 1 triangle in the bottom-left of the right-vertical quadrant, and 1 triangle in the bottom-right corner. Total: 4 individual triangles.
Identify Composite Triangles
Look for triangles formed by combining smaller regions: 1 triangle is formed by the top-left and middle-left regions, 1 triangle by the bottom-right and middle-right regions, and 1 large triangle is formed by the entire diagonal path. Total: 3 composite triangles.
Final Summation
Adding the individual triangles (4) and the composite triangles (3) gives a total of 7 triangles.
A: 8 is incorrect because there is no 8th triangle hidden in the geometry. B: 9 is incorrect because it exceeds the total identifiable set. D: 10 is incorrect as it overestimates the geometric partitions present in the figure.
C is correct because a rigorous manual count of all small and composite geometric triangles yields exactly 7.
When counting triangles in complex grid figures, always mark the triangles as you count them to avoid double-counting or missing overlapping shapes.
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