Question

Hi can someone please help me? :( im not sure where im going wrong. ty!!

Answer 1

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 ,

$AB^2 - BC^2 = AC^2$

$\sqrt{64 - 16} = AC$

AC =4 $\sqrt3$

shade region area = area of semicircle - area of triangle

= $1/2 \pi r^2$ - 1/2 × base × height

=1/2 × 16 $\pi$ - 1/2 × 4 × $4\sqrt3$

=8$\pi$ - 8$\sqrt3$

=8($\pi - \sqrt3$)