find the area of the region overlapped by the 2 semi circles

Asked by geethika | 11th Feb, 2010, 05:29: AM

Expert Answer:

Area of black shaded area = 2xarea of segment ABC as shown.

Area of segment ABC = area of sector ABCD - 2xarea of triangle AOD

AB = BC = CD = AD = Radius of the circle = 4 cm.

Hence ABCD is a rhombus, the diagonals bisect, therefore DO = OA = 2 cm, since AD = 4 cm.

Now, AO = (AD2-OD2) = 23 cm ............Pythagorus's theorem.

Also cos ADO = 2/4 = 1/2, therefore ADO = 60, and ADC = 120 = 2π/3

Area of segment ABC = area of sector ABCD - 2xarea of triangle AOD

= πR2/3 - 2 x 1/2 x DO x OA

= π42/3 - 2 x 1/2 x 23 x 2

= 9.83 cm2

Area of shaded area required = 2x9.83 = 19.66 cm2

Regards,

Team,

TopperLearning.

 

 

Answered by  | 12th Feb, 2010, 02:17: PM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.