Answer :

Given, AC = 6cm and BC = 8 cm


A triangle in a semi-circle with hypotenuse as diameter is right angled triangle.


In right angled triangle ACB,


(AB)2 = (AC)2 + (CB)2


(By Pythagoras theorem)


(AB)2 = (6)2 + (8)2


(AB)2 = 36 + 64


(AB)2 = 100 (AB)= 10


Diameter of the circle = 10 cm


Thus, Radius of the circle = 5 cm


Area of circle = πr2


= π(5)2


= 25π cm2


= 25 × 3.14 cm2


= 78.5 cm2


Also, Area of the right angled triangle = (1/2) × Base × Height


= (1/2) × AC × CB


= (1/2) × 6 × 8 = 24 cm2


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


= (78.5-24)cm2


= 54.5cm2


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