Find the number of triangles in the given figure.

For a compound figure built from smaller triangular pieces, count triangles by complexity level: first the simplest (single-piece) triangles, then triangles formed by combining two pieces, three pieces, and so on, up to the largest triangle made of all pieces. Summing every level's count gives the total, provided each distinct triangle is counted exactly once.

1. Label every vertex and internal intersection point of the figure (A at the apex; H, B on the upper sides; G, C on the middle sides; F, E, D along the base; I, J as the interior intersection points).

2. Single-piece (simplest) triangles: AHB, GHI, BJC, GFE, GIE, IJE, CEJ, CDE — 8 triangles.

3. Two-piece triangles: HEG, BEC, HBE, JGE, ICE — 5 triangles.

4. Three-piece triangles: FHE, GCE, BED — 3 triangles.

5. Four-piece triangle: AGC — 1 triangle.

6. Nine-piece (largest) triangle: AFD, the whole outer triangle — 1 triangle.

7. Total = 8 + 5 + 3 + 1 + 1 = 18.

As an independent check, group the same 18 triangles by orientation (upward-pointing vs. downward-pointing) instead of by size — every triangle identified above points the same way as its constituent smallest pieces, and no triangle appears in more than one size-group, confirming none was double-counted or missed.

So the figure contains 18 triangles in total.