Find the radius of the incircle of a regular hexagon of side 24cm.

Let AB be the side of the regular hexagon and let O be the centre of the incircle.

Draw OC perpendicular to AB.

If r is the radius of the circle, then OC = r.

We know that total sum of angles of a regular polygon = 360°

So, ∠AOB = = 60°

∴ ∠AOC = = 30°

⇒ tan 30° =

⇒ =

⇒ r = 12 × 1.732 = 20.784 cm

Hence, radius of incircle is 20.784 cm.