How many triangles are there in the following figure?

The correct answer is Option (1) → 18

To count triangles without missing or repeating any, letter every point where lines meet and count by size, from the smallest triangles to the largest. Three letters form a triangle only when each pair of them is joined by a line of the figure.

The smallest triangles (no line inside them):

• Upper half: ABE, ADE, BEF, BCF, CFG — 5

• Lower half: DEH, EHI, EFI, FIJ, FGJ — 5

Triangles made of two small ones (on the side edges):

• AEH and CFJ — 2

Triangles made of three small ones (a side edge and one long slanting line):

• ABH, AHI, CBJ, CIJ — 4

The largest triangles (a full edge of the rectangle and two long slanting lines):

• ACI and HJB — 2

Total \(=10+2+4+2=18\) triangles.