Is this statement true or false?
The side length of a regular hexagon is equal to the length of the radius.

Question

Is this statement true or false? The side length of a regular hexagon is equal to the length of the radius.

UpStudy AI · Accepted Answer

**True.**

In a regular hexagon (a six-sided polygon with all sides and angles equal), the relationship between the side length and the radius is direct. Here's why:

- **Circumradius Definition:** The radius (often referred to as the circumradius in the context of polygons) is the distance from the center of the hexagon to any of its vertices.

- **Mathematical Relationship:** For a regular $$ n $$-sided polygon, the side length $$ s $$ and the circumradius $$ R $$ are related by the formula:
  $$
  s = 2R \sin\left(\frac{\pi}{n}\right)
  $$
  
  Substituting $$ n = 6 $$ for a hexagon:
  $$
  s = 2R \sin\left(\frac{\pi}{6}\right) = 2R \times \frac{1}{2} = R
  $$
  
  This shows that the side length $$ s $$ is equal to the circumradius $$ R $$ in a regular hexagon.

Therefore, the statement "The side length of a regular hexagon is equal to the length of the radius" is **true**.
The side length of a regular hexagon is equal to the length of the radius.

Is this statement true or false?
The side length of a regular hexagon is equal to the length of the radius.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Geometry Questions