The triangle ABC is a right angled triangle , right angled at C because it is the angle subtended by the diameter
Now OA = OB = OC = 4 cm (radii)
AB = OA + OB = 8 cm
By pythagoras theorem ,
[tex]AB^2 - BC^2 = AC^2[/tex]
[tex]\sqrt{64 - 16} = AC[/tex]
AC =4 [tex]\sqrt3[/tex]
shade region area = area of semicircle - area of triangle
= [tex]1/2 \pi r^2 [/tex] - 1/2 × base × height
=1/2 × 16 [tex]\pi[/tex] - 1/2 × 4 × [tex]4\sqrt3[/tex]
=8[tex]\pi[/tex] - 8[tex]\sqrt3[/tex]
=8([tex]\pi - \sqrt3[/tex])
