Find the number of triangles in the given figure.

To count triangles in a compound figure, classify every triangle by how many elementary triangular regions combine to form it (1, 2, 3, 6, 12, and so on, based on the figure's symmetry), count each class exactly once without overlap, then add all the classes together for the total.

The figure may be labelled as shown.

• Simplest triangles (one elementary region each): AML, LRK, KWD, DWJ, JXI, IYC, CYH, HTG, GOB, BOF, FNE, EMA — 12 triangles.

• Triangles combining two regions each: AEL, KDJ, HIC, FBG — 4 triangles.

• Triangles combining three regions each: APF, EQB, BQH, GVC, CVJ, IUD, DUL, KPA — 8 triangles.

• Triangles combining six regions each: ASB, BSC, CSD, DSA, AKF, EBH, CGJ, IDL — 8 triangles.

• Triangles combining twelve regions each: ADB, ABC, BCD, CDA — 4 triangles.

Total number of triangles in the figure = 12 + 4 + 8 + 8 + 4 = 36.

Cross-check: the figure has four-fold symmetry (four large outer triangles arranged around a central point), so each symmetric class should appear in multiples of 4 — and every category above (12, 4, 8, 8, 4) is indeed a multiple of 4, confirming the count is complete with no double-counting.