Question

1. if a circle has a radius ( r ) and an inscribed regular hexagon, what is the perimeter ( p ) of the hexagon?

( \boldsymbol{\text{a. } p = 6r} )
( \boldsymbol{\text{b. } p = 3r} )
( \boldsymbol{\text{c. } p = 12r} )
( \boldsymbol{\text{d. } p = 4r} )

Explanation:

Step1: Analyze the regular hexagon inscribed in a circle

A regular hexagon inscribed in a circle means that the radius of the circle is equal to the length of each side of the regular hexagon. Let the side length of the hexagon be \( s \), so \( s = r \).

Step2: Calculate the perimeter of the regular hexagon

The perimeter \( P \) of a regular hexagon is given by the formula \( P = 6\times s \), where \( s \) is the length of each side. Since \( s = r \), we substitute \( s \) with \( r \) in the formula. So \( P = 6\times r = 6r \).

Answer:

A. \( P = 6r \)