In a regular hexagon ABCDEF, find AB if AD = 24.

The segment AD connects the opposite vertices of the hexagon and is the diameters of the circle circumscribed around it. AD = D = 24 cm.Then R = D / 2 = 24/2 = 12 cm.

Let’s draw the radius of the OB of the circle. Since all sides of a regular hexagon are equal, they divide the circle into six equal arcs. The degree measure of each arc is 360/6 = 60.

Then in triangle AOB the central angle AOB = 60, and since OA = OB = R, then triangle AOB is equilateral, OA = OB = AB = R.

Then AB = AD / 2 = 24/2 = 12 cm.