UPSC Civil Services 2011 Prelims General Studies Paper II

Let the side of the smallest triangle be 1 unit, then:
number of the smallest triangle (with side 1 unit) = 12
number of triangles with side 2 units = 7
number of triangles with side 3 units = 3
number of triangles with side 4 units = 1
Total number of triangles in given grid = 12 + 7 + 3 + 1 =23