A regular polygon has six axes of symmetry.what is name of this shape?

A regular hexagon has six axes of symmetry. Three join opposite corners, and three join the midpoints of opposite sides.

a hexagon

To determine the name of a regular polygon with six axes of symmetry, we can start by understanding what axes of symmetry are.

Axes of symmetry are imaginary lines that pass through the center of a shape and divide it into two congruent halves. In regular polygons, these axes can be rotational or reflectional.

A regular polygon with six axes of symmetry would have six lines passing through its center, dividing it into six congruent halves.

Now, let's think about which regular polygons have this property. To do this, we can consider each regular polygon and count the number of possible axes of symmetry.

Starting with a triangle, it has three sides, but no axis of symmetry can divide it into six congruent halves.

Moving on to a quadrilateral (a square), we have four sides. We can see that it has four axes of symmetry, but not six.

Next, considering a pentagon, we have five sides. Again, we find that it has five axes of symmetry but not six.

Finally, let's focus on a hexagon. A hexagon has six sides, and we can clearly see that it has six axes of symmetry, each dividing it into six congruent halves.

Therefore, the name of the regular polygon with six axes of symmetry is a hexagon.