Area of the shaded segment=

Question

asked Jul 4, 2020 85.3k views

2 Answers

Craig Fisher · Answer 1 · 2020-07-05T07:28:48+0000

Answer:

A

Explanation:

The area of the shaded segment

= area of sector OAB - area of ΔOAB

area of sector = area of circle × fraction of circle, that is

A = πr² × fraction of circle

= π × 6² ×
(60)/(360)

= 36π ×
(1)/(6) = 6π units²

Area of triangle = 0.5 × 6 × 6 × sin60° = 18 ×
(√(3) )/(2) = 9
√(3) units²

Hence

area of shaded segment = 6π - 9
√(3) units² → A