Question

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

"Find the area of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximations)."

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`

`√(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`)