Question

consider a regular hexagon inscribed in circle c with radius r. regular hexagons have six congruent sides and six congruent angles. in the figure, angle cab measures 60°. what is m∠acb? 60° what is the length of segment ab? r what is the perimeter of the hexagon? 6r the perimeter of the hexagon is slightly less than the circumference of the circle. the circumference of the circle is slightly greater than 6r slightly less than 6r equal to 6r

Explanation:

Step1: Recall the formula for the circumference of a circle

The formula for the circumference \( C \) of a circle with radius \( r \) is \( C = 2\pi r \).

Step2: Compare \( 2\pi r \) with \( 6r \)

We know that \( \pi\approx3.14 \), so \( 2\pi\approx6.28 \). Then \( 2\pi r\approx6.28r \), which is slightly greater than \( 6r \) (since \( 6.28>6 \)).

Answer:

slightly greater than \( 6r \)