Answer :

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,

BA^{2} = CB^{2} + AC^{2}

⇒ BC^{2} = 36 + 64

⇒ BC = 10 cm

⇒ Area of ∆ABC = 24 cm^{2}

Radius of the circle = 5 cm

Area of a circle = πr^{2}

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

⇒ Area of the shaded region = 78.57 -24 = 54.57 cm^{2}

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