Answer: The area of the shaded segment = 9.822 square miles
Step-by-step explanation:
The area of the shaded segment = Area of sector - area of triangle
The formula for determining the area of a sector is expressed as
Area of sector = θ/360 × πr²
Where
θ represents the central angle.
r represents the radius of the circle.
π is a constant whose value is 3.14
From the information given,
r = 4 miles
θ = 120 degrees
Area of sector = 120/360 × 3.14 × 4²
Area of sector = 16.75 square miles
The formula for determining the area of a triangle is expressed as
Area = 1/2abSinC
Where
a and b are lengths of the given sides.
C is the given angle
Area = 1/2 × 4 × 4 × Sin120
Area = 8 × 0.866 = 6.928 square miles
Therefore, the area of the shaded segment = 16.75 - 6.928 = 9.822 square miles
