Detailed Explanation:

Step 1 – Identify base triangles from diagonals: The two diagonals PR and QS intersect at point O, creating 4 base triangles: △POQ, △QOR, △ROS, △SOP.

Step 2 – Count triangles formed by vertical line through O: The vertical line through O divides the rectangle, creating 4 additional triangles by combining adjacent base segments.

Step 3 – Count triangles formed by horizontal line through O: The horizontal line through O similarly creates 4 more triangles by combining base segments.

Total count: 4 (diagonal intersections) + 4 (vertical line combinations) + 4 (horizontal line combinations) = 12 triangles.