Question

complete the sentence.
the intersection of a square and a regular hexagon can be ______.
a pentagon two points
two trapezoids a parallelogram

Explanation:

To determine the intersection of a square and a regular hexagon, we analyze the possible shapes formed by their overlapping regions. A square has four sides, and a regular hexagon has six sides. When they intersect, the overlapping area can form a pentagon. Let's analyze the other options:

• "two points": The intersection of two polygons (a square and a regular hexagon) is typically a region with area (a polygon) rather than just two points, as polygons are closed figures with area, so this is unlikely.
• "two trapezoids": The intersection of two simple polygons (square and regular hexagon) is a single polygon (or empty set), not two separate trapezoids, as the intersection region is connected.
• "a parallelogram": A square is a type of parallelogram, but the intersection of a square and a regular hexagon doesn't typically form a general parallelogram (other than the square itself in some cases, but the most probable non - trivial intersection shape among the options is a pentagon. When the square and hexagon overlap in a way that the square cuts off one corner of the hexagon (or vice - versa) in a non - symmetric way, the intersection can be a pentagon.

Answer:

a pentagon