Question

Please help and show all work. 20 points.

Answer 1

The area of the 120° sector is
.. Asector = (1/2)r^2*θ . . . . . . . angle in radians
.. = (1/2)*(24 m)^2*(2π/3)
.. = 192π m^2

The area of the white triangle in that sector is
.. Atriangle = (1/2)r^2*sin(θ)
.. = (1/2)*(24 m)^2*(√3)/2
.. = 144√3 m^2

The area of the shaded segment is the difference of these
.. Asegment = Asector -Atriangle
.. = (192π -144√3) m^2

The 2nd selection is appropriate.