Find the number of triangles in the given figure.

Concept: To count every triangle in a compound figure, first identify every simplest (undivided) triangle. Then find every larger triangle formed by combining two or more simplest triangles, grouping them by how many simplest triangles each one contains. The total is the sum of every group's count, with each triangle counted only once.

Application: Label the figure as shown, then work through it group by group, from the smallest triangles to the largest.

1. Simplest (single-unit) triangles: BFG, CGH, EFM, FMG, GMN, GHN, HNI, LMK, MNK and KNJ — 10 triangles.

2. Triangles made of three simplest units: FAK and HKD — 2 triangles.

3. Triangles made of four simplest units: BEN, CMI, GLJ and FHK — 4 triangles.

4. Triangles made of eight simplest units (the two full-height triangles spanning the figure): BAJ and CLD — 2 triangles.

Adding every group: 10 + 2 + 4 + 2 = 18 triangles in total.

Cross-check: the figure is left-right mirror-symmetric (B swaps with C, A with D, L with J, E with I, F with H, M with N; G and K lie on the axis of symmetry). Under this mirror, every triangle in each group either pairs with another member of the same group or maps to itself — for example BFG pairs with CGH, LMK pairs with KNJ, GLJ and FHK each map to themselves, and BAJ pairs with CLD. Since every triangle is accounted for by this pairing with none left over, no triangle in any group has been missed or double-counted.