Q8 of 31 Page 183

In the given figure, AB is a diameter, AC = 6 cm, BC = 8 cm. Find the shaded region.

Given:


In ∆ABC,


AC = 6 cm, BC = 8 cm


Also, ∠C = 90° because angle subtended by the diameter is 90° and AB is the diameter.


By Pythagoras theorem,


BA2 = CB2 + AC2


⇒ BC2 = 36 + 64


⇒ BC = 10 cm




⇒ Area of ∆ABC = 24 cm2


Radius of the circle = 5 cm


Area of a circle = πr2



Area of the shaded region = Area of circle –Area of the triangle


⇒ Area of the shaded region = 78.57 -24 = 54.57 cm2


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