Question

Find the area of a right hexagon inscribed in a circle having 14 cm of radius.

Answer 1

Radius of circle = OA = OB = OC = OD = OE = OF = 14 cm

AOB = 360/6 = 60° 

∴ In ΔAOB AO = BO = 14 cm 

∠AOB = 60° 

then ∠OAB = ∠OBA 

(∵ Opposite to equal sides) 

And ∠OAB + ∠OBA + 60 = 180 

⇒ ∠OAB = ∠OBA = ∠AOB = 60° 

Hence it is an equilateral triangle. 

∴ OA = OB = AB = 14 cm 

∴ Area of hexagon = 6 (Area of ΔAOB)