find the area of the shaded region

Asked by debasish2345 | 26th Nov, 2009, 08:32: AM

Expert Answer:

Let C and D be the centre of the circle where AD = 12cm and BC = 4 cm

In triangle CDE,

CD2 = DE2 + CE2

CE2 = CD2 - DE2

CE2 = 162 - 82 = 192

So, CE = 83

i.e Height of the trapezium, h = 83

Area of the trapezium = 1/2 x (BC + AD) x h

                                       = 1/2 x 16 x 83

                                       = 643 cm2

In triangle CDE, 

tan x = 83  / 8

x = 60o

So, FCE = 30o          

i.e BCF = 90o + 30o = 120o   

Now, Area of sector ADF =   x (12)2 x (60/360) = 75.36 cm2

Now, Area of sector BFC =   x (4)2 x (120/360) = 16.74 cm2

Area of shaded region =Area of Trapezium ABCD - (Area of Sector ADF + Area of Sector BFC)

                                     = 643 - (75.36 + 16.74)  = 18.75 cm2

 

   

       

Answered by  | 11th Dec, 2009, 02:51: PM

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