Step One
Find the area of the entire sector.
Formula
Area Sector = (given angle / 360) * π * r²
r = 24
given angle = 120°
Area Sector = (120/360) * π 24²
Area Sector = 1/3 * π 576
Area Sector = 192 π
Step Two
Find the length and height of the triangle.
Draw and angle bisector for the 120° angle. What you get is 2 (congruent) 30 - 60 - 90 triangles. The side adjacent to the 60° angle is 1/2 the size of the hypotenuse. (Don't look at the diagram. It's not to scale).
The side opposite a 60° angle is (√3/2) * hypotenuse
The side opposite = (√3 /2) 24 = 12 * √3
The base of the triangle = 2 * 12* √3 = 24 * √3
Step Three
Find the area of the Triangle
h = 12
b = 24*√3
Area = 1/2 * b * h
Area = 1/2 * 24√3 * 12
Area = 144 * √3
Step Four
Find the area of the shaded part.
Area = Sector area - Triangle Area
Area = 192 π - 144 * √3 m^2 <<<<<<< Answer
B <<<<<< Answer