Find the number of triangles in the adjoining figure:

Answer: 24 triangles.

Step-by-step counting (label the rectangle's corners as A = top-left, B = top-right, C = bottom-right, D = bottom-left; let P be the interior point near the top-left side, Q be the interior point near the bottom-right side, and O be the central intersection where the internal lines cross).

• Smallest triangles (corner-based small triangles): Each corner area has two small triangles formed by the corner, the nearby interior point, and the central intersection. There are 4 corners × 2 = 8 smallest triangles.

• Medium triangles (formed by joining two adjacent smallest triangles): In each corner region the two adjacent smallest triangles can combine to form medium-sized triangles whose base spans a short internal segment. Counting these across the figure gives 8 medium triangles.

• Larger triangles using an interior point as a vertex: There are triangles that have P or Q as an apex and use corners and the central intersection as other vertices. Counting all distinct such triangles yields 6 larger triangles.

• Largest triangles that span the figure: There are 2 largest triangles formed by the major spanning lines (each uses two opposite corners and the central line structure).

Total triangles = 8 (small) + 8 (medium) + 6 (larger) + 2 (largest) = 24.

Tip: When counting triangles in such figures, systematically classify triangles by size or by which special point is their apex (corner, interior point, or central intersection). This avoids double-counting and ensures none are missed.