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°. 1. What is m∠ACB? 2. What is the length of segment AB? 3. What is the perimeter of the hexagon? 4. The perimeter of the hexagon is ___ the circumference of the circle. 5. The circumference of the circle is ___.

Answer 1

1. 60°

2. r

3. 6r

4. slightly less than

5. slightly greater than 6r

Explanation:

1. It is stated.

2 & 3. If there are 6 of the arcs and one arc is measured as r, then the perimeter is 6r.

4. The perimeter is slightly less than because the circumference is longer.

5. Use the inverse of 4.