Answer:
1.4 m²
Step-by-step explanation:
The area of a sector with central angle θ (in radians) is given by the formula
A = (1/2)r²θ
The area of the triangle with central angle θ is given by the formula
A = (1/2)r²sin(θ)
The area of the shaded segment is the difference of these:
A = (1/2)r²(θ -sin(θ))
Your segment has a central angle of 60° = π/3 radians, so its area is ...
A = (1/2)(4 m)²(π/3 -sin(π/3)) = (8 m²)(π/3 -(√3)/2)
A ≈ 1.4 m²
The area of the shaded segment is about 1.4 m².
