points SAlgTrig3 63060 My Notes A WebAssign Plot Find the ar

points SAlgTrig3 6.3.060 My Notes A WebAssign Plot Find the area of the shaded region in the figure. (Round your answer to one decimal place.) 3 16 Need Help?Read ItTalk to a Tutor Submit Answer Save Progress

Solution

1) Find the area of triangle with central angle= pi/3

Its an isosceles triangle :

Area = (1/2)*16*16sin60 = 128sin60 = 110.85

Areaof major sector = area of circle - area of sector with angle 60 deg

= pi(16)^2 - pi*(60/360)*16^2

= pi16^2[ 1 - 1/6]

= pi*16^2(5/6)

= 670.20

Area of pink region: = 670.20 + 110.85 = 781.05 = 781.1 units

2) First find the area of isosceles triangle

Area of triangle = (1/2)*4*4*sin120 = 6.93

Now to find the shaded are = Area of sector with angle 120 - area of triangle

= (120/360)*pi*4^2 - 6.93

= 9.825 = 9.83 units