Question

Find the exact area of the shaded region.

A) (192pi-144) m^2
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B)(192pi-144 V3 ) m^2
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C)(8pi144 V 3 )
D) none of the above
SEE ATTATCHMENT

Answer 1

Central Angle between two radii=120°

Radii of the circle = 24 m

When two sides of triangle are equal ,then angle opposite to them are equal.

120 + 2* (Measure of the angle )=180°

Measure of the two angles of the triangle
`=(60 degree)/(2)\\\\=30 degree`

`Sin 30=(P)/(24)\\\\B=12 \\\\ Cos 30=(B)/(24)\\\\B=12 √(3)`

Base = 2*12√3=24√3 meter

Altitude of Triangle = 12 meter

Area of Shaded Region

= Area of Sector - Area of Triangle

`=(\pi *24*24*120)/(360)- (1)/(2)*24√(3)*12\\\\=192*\pi  - 144*√(3)`

Option B: (192 pi-144 √3 ) m²