What is the minimum number of straight lines that is needed to construct the…

Concept: In a composite figure, count DISTINCT straight lines, not drawn segments. Two segments that lie in the same direction and meet at a shared vertex are really one continuous straight line (for example, a square's diagonal can run straight on into the side of an adjoining triangle). So group every stroke by direction — horizontal, vertical, each slanting direction — and count once per distinct line.

The figure may be labelled as shown.

Applying this to the figure:

1. Horizontal lines: A-C-E (the top row of the two squares) and J-H-F (the bottom row) — 2 lines.

2. Vertical lines: A-J, C-H and E-F — 3 lines.

3. Slanting lines: in each square, one diagonal runs straight on into the side of the triangle capping the OPPOSITE square, so the diagonal and that triangle side are a single continuous line — this gives four such long lines. The remaining side of each of the four triangles does not continue into anything else, giving four standalone lines. Total slanting lines = 4 + 4 = 8.

4. Total straight lines needed = 2 (horizontal) + 3 (vertical) + 8 (slanting) = 13.

Cross-check: counted segment by segment (without merging), the two squares contribute 4 diagonal segments and the four triangles contribute 8 side segments — 12 slanting segments in all. Since 4 of those diagonal segments are collinear continuations of 4 triangle-side segments, they collapse into 8 distinct slanting lines, not 12. Adding the 2 horizontal + 3 vertical boundary lines confirms 5 + 8 = 13 straight lines overall.

So the minimum number of straight lines needed to construct the figure is 13.