Question

What is the area of the shaded region in the given circle in terms of and in simplest form?

60
12 m
OA (120 +6,√3) m²
B. (96x +36√√3) m²
OC. (120x +36 √3) m²
OD. (96* +6√3) m²

Answer 1

c) (120π + 36√3) m²

Explanation:

ar(shaded region) = ar(circle) - ar(segment)

= ar(circle) - [ar(sector) - ar(triangle)]

= ar(circle) - ar(sector) + ar(triangle)

`= \pi r^2 - (\theta)/(360)\pi r^2 + (√(3) )/(4) r^2\\\\=r^2[\pi - (\theta)/(360)\pi +(√(3) )/(4) ] \\\\=r^2[\pi[1 - (\theta)/(360)] +(√(3) )/(4) ] \\\\=12^2[\pi[1 - (60)/(360)] +(√(3) )/(4) ] \\\\=144[\pi[1 - (1)/(6)] +(√(3) )/(4) ] \\\\=144[\pi[(5)/(6)] +(√(3) )/(4) ] \\\\=144((5)/(6)) \pi +144((√(3) )/(4) ) \\\\=24(5)\pi +36√(3) \\ \\=120\pi + 36√(3)`