Question

Find area of shaded region. Round to the nearest tenth need help ASAP

Answer 1

The area of shaded region is 226.4 meter squared.

Explanation:

Radius of the circle = r =18.6 m

Angle subtended by chord
`\theta = 123^o`

Area of sector =
`(\theta )/(360^o)\pi r^2`

In ΔOAB

∠A+∠B+∠O= 180°

2∠A+123°= 180°(∠A=∠B, isosceles triangle)

∠A=∠B=28.5°

AC=BC (Radius of the circle bisects the chord at right angle.)...(1)

In ΔOAC

`\sin 123^0=(OC)/(OA)`

OC = 8.87 m

`\cos 123^0=(AC)/(OA)`

AC = 16.34 m

AB = AC+AB=16.34 m+16.34 m=32.68 m (from (1))

Area of the ΔOAB =
`(1)/(2)* OC* AB`

=
`(1)/(2)* 8.87 m* 32.68 m=144.93 m^2`

Area of segment = Area of sector - Area of triangle:

`371.34 m^2-144.93 m^2=226.41 m^2\approx 226.4 m^2`

The area of shaded region is 226.4 meter squared.