Comparing Perimeter of Hexagon and Circumference of Circle

Consider a regular hexagon inscribed in a circle with a radius of 10 units. Each side of the hexagon is thus equal to the chords of the circle drawn between adjacent vertices.

To find the length of each side of the hexagon, use the chord length formula, which is given by:

$$ L = 2r imes ext{sin}igg(rac{ heta}{2}igg) $$

where $L$ is the length of the chord (side), $r$ is the radius of the circle, and $\theta$ is the central angle in radians that subtends the chord. For a regular hexagon, the central angle $\theta$ is:

$$ \theta = \frac{360^{\circ}}{6} = 60^{\circ} $$

Given this situation, calculate the length of one side of the hexagon. Then, determine whether the perimeter of the hexagon is greater than the circle's circumference.