How many triangles are there in the given figure?

Concept: To count every triangle in a compound figure, first mark out each smallest non-overlapping triangular region, then check whether any set of two or more adjacent regions together forms a larger triangle — a valid triangle must be bounded only by straight sides meeting at exactly three vertices. A region with a curved edge or four straight sides is never a triangle, no matter how it looks.

Application: Label the outer figure with apex T (top), L (left), B (bottom) and R (right). A vertical line from T to B splits the kite-shaped outline into two large triangles. A shorter line inside the left large triangle, drawn parallel to TB, cuts off a smaller triangle near the tip at L. Below B, two extra straight lines mark off a small triangle hanging beneath the main shape. A semicircular arc is also drawn using the edge TR as its diameter, bulging outward.

1. The large triangle formed on the left of the central vertical line, bounded by the left edge, the lower-left edge and the vertical line.

2. The large triangle formed on the right of the central vertical line, bounded by the upper-right edge, the lower-right edge and the vertical line.

3. The small triangle nested at the leftmost tip, cut off by the short internal line drawn parallel to the central vertical line.

4. The small triangle attached beneath the main shape, formed by the two extra straight lines below the bottom vertex.

The remaining four-sided strip between the nested tip triangle and the central vertical line has four straight sides, and the semicircular patch has a curved boundary — neither qualifies as a triangle, so they add nothing further to the count.

Cross-check: Grouping differently confirms the same total: the two large triangles on either side of the central line give 2, and the two small triangles (the nested tip triangle and the attached lower triangle) give another 2, for 2 + 2 = 4 triangles in all.