OAB is an equilateral triangle with each angle equal to
60∘.
Area of the sector is common in both.
Radius of the circle = 6 cm.
Side of the triangle = 12 cm.
Area of equilateral
Δ =√34×(side)2 Area of the equilateral triangle
=√34×(OA)2=√34×144=36√3 cm2 Area of the circle
=
πR2=227×62=7927 cm2 ![](https://search-static.byjusweb.com/question-images/byjus/_482b3bc94b85bb9a90efe8ea59c161a4f6698d8320160914-11091-uspqm0.png)
Area of the sector making angle
θ =(θ360∘)×πr2 Area of the sector making angle
60∘ =(60∘360∘)×πr2 cm2 =16×227×62 cm2=1327 cm2 Area of the shaded region= Area of the equilateral triangle + Area of the circle - Area of the sector
=36√3 cm2+7927 cm2−1327 cm2 =(36√3+6607) cm2