Calculate the area of the shaded region? This question please about radians, i would appreciate your help

Question

3059 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-26T16:27:25

Area of shaded region is #8.876# #cm^2#

If we join #OA#, #DeltaOAB# is right angled triangle at #/_B# and #/_BOA=pi/3=60^o# and #/_BAO=pi/6=30^o#

hence #BA=3.6xxsqrt3# #cm.#

and as area of a right triangle is half the product of its legs forming right angle,

area of #DeltaOAB=(3.6xx3.6xxsqrt3)/2=3.24xxsqrt3=11.224# #cm^2#

Hence area of quadrilateral is #2xx11.224=22.448# #cm^2#

Now area of sector (this is one-third of circle of radius #3.6# #cm,#)
is

#1/3xxpixx3.6xx3.6=3.1416xx1.2xx3.6=13.572# #cm^2#

Hence area of shaded region is #22.448-13.572=8.876# #cm^2#.