CBSE Class 10 Answered
find the area of the region overlapped by the 2 semi circles
Asked by geethika | 11 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 | 12 Feb, 2010, 02:17: PM
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