What is the area of the shaded segment?

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