Answer: option 3 is the correct answer.
Step-by-step explanation:
The formula for determining the area of a sector is expressed as
Area = 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°
Area of sector = 120/360 × 3.14 × 4²
= 16.75 square miles
To determine the area of ∆ABC, we would apply the formula,
Area of triangle = 1/2abSinC
From the information given,
a = 4
b = 4
C = 120°
Therefore,
Area = 1/2 × 4 × 4 × Sin120
Area = 8 × Sin120 = 6.92 square miles. Therefore area of the segment is
16.75 - 6.92 = 9.83 square miles
