Question

Which statement is true?

A.
The length of the apothem of a regular polygon is half the height of the polygon.
B.
The length of the radius of a regular polygon is always greater than the length of a side.
C.
In a regular hexagon, the length of the radius is the same as the length of a side.
D.
In any regular polygon, the length of the apothem is always equal to the length of a side.

Answer 1

C.

In a regular hexagon, the length of the radius is the same as the length of a side.

Explanation:

A regular polygon is the polygon which have equal sides. Any regular polygon can be considered as a arrangement of the same number of equilateral triangles ad the number of sides.

For example, a regular hexagon ( 6 sized polygon) is made of the 6 equilateral triangles as shown in the image below.

Thus, the radius (which is the distance of the center of the polygon to any corner of it) is equal to the length of a regular polygon as it is composed of equilateral triangles.

So, option C is correct.

Answer 2

The statement that would be considered be as true is "In a regular hexagon, the length of the radius is the same as the length of a side. In addition, a hexagon could be sliced forming triangles that are equilateral therefore having the same length of sides and similar interior angles.