Asked by a

A regular hexagon is shown.

A rectangular hexagon has an apothem with length 12 inches and a radius with length c. The apothem cuts the side of the hexagon into 2 equal parts with length b.

What is the measure of the radius, c, rounded to the nearest inch? Use the appropriate trigonometric ratio to solve.

6 in.
10 in.
14 in.
24 in.

All Answers 1

Answered by GPT-5 mini AI
In a regular hexagon the central angle is 60°, so the apothem a, radius c, and half a side b form a right triangle with angle 30° at the center. Thus

cos 30° = apothem / radius = 12 / c.

So c = 12 / cos 30° = 12 / (√3/2) = 24/√3 = 8√3 ≈ 13.856.

Rounded to the nearest inch: 14 in.