Question

what is the difference between constructing a square and constructing a regular hexagon? (1 point)the diameter of the circle is used for the square construction, but the radius of the circle is used for the regular hexagon construction.the radius of the circle is used for the square construction, but the diameter of the circle is used for the regular hexagon construction.the square will need two arcs along the circle, but the hexagon will need two arcs above and two arcs below the diameter of the circle.the square will need six arcs along the circle, but the hexagon will need two arcs above and two arcs below the diameter of the circle.

Answer 1

The difference between constructing a square and a regular hexagon lies in the use of the circle's radius or diameter. For a square, the side lengths equal the diameter of the circle, while for a hexagon, the side lengths match the circle's radius. Hexagonal packing is also more space-efficient compared to square packing.

Step-by-step explanation:

The primary difference between constructing a square and constructing a regular hexagon relates to the use of a circle's radius (r) and diameter (2r). When constructing a square, each side of the square equals the diameter of the circle, which is twice the length of the radius. In contrast, when constructing a regular hexagon, each side of the hexagon equals the radius of the circumscribed circle. Additionally, for a hexagon, you can place six arcs around the circle, each arc being equal in length to the radius, to determine the vertices of the hexagon.

In terms of packing efficiency, a hexagonal-packed arrangement is more space-efficient than a square-packed arrangement. While square packing covers 78 percent of the area, hexagonal packing yields 91 percent coverage, demonstrating the more efficient use of space in the hexagonal grid.