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Area of the shaded segment=

Area of the shaded segment=-example-1
Area of the shaded segment=-example-1
Area of the shaded segment=-example-2
Area of the shaded segment=-example-3
Area of the shaded segment=-example-4

2 Answers

5 votes

Answer: 6π-9√3 unit²

Explanation:

area of sector OBAO =Area of circle/6 (∵ 60°=360°/6)

= π×6²/6

= 6π unit²

now, area of triangle OAB=√3×6²/4 (∵ it is an equilateral triangle and area of equilateral triangle=√3×side²/4)

=9√3 unit²

Area of shaded region= area of sector OBAO- area of triangle OAB

= 6π-9√3 unit²

User Mouna Cheikhna
by
8.2k points
7 votes
Alright, since the radius is 6, pi(6)^2=36pi is your area. Since 60/360=1/6, that means the overall section is 36pi/6=6pi. Since this can be made 6 times,
AB = 6 as 36/6=6 and OAB is equilateral, making the area of that
sqrt(3)*(6^2)/4 = 9sqrt(3). Therefore, the area of the shaded segment is
6pi-9sqrt(3)
User Kilsy
by
8.6k points

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