Find the area of the shaded segment of the circle.

(Round to the nearest tenth as needed.)

Area of the shaded region = 87.5 cm²

Step-by-step explanation:

Area of the shaded region = Area of the sector - Area of the triangle

Area of the sector =

Here, θ = Central angle subtended by the arc

r = radius of the circle

Area of the given sector =

                                         = 48π

                                         = 150.796 cm²

From ΔABC,

Central angle BAC = 120°

Since, AD is an angle bisector of ∠BAC,

m∠BAD = m∠CAD = 60°

∠ADC = 90° [By theorem, line from the center to any chord is a perpendicular bisector of the chord in a circle)

Now,  cos(60) =

AD = 6

Similarly, sin(60) =

DC =

Since, BC = 2(DC) =

Area of ΔABC =

                        =

                        =

                        = cm²

                        = 62.35 cm²

Now area of the shaded region = (150.796 - 62.35)

                                                     = 87.456

                                                     ≈ 87.5 cm²

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