Answer:
B: 192pi - 144
Step-by-step explanation:
Area of the sector = (120/360) * pi * r^2
Area of the sector = 1/3 * pi * 24 * 24
Area of the sector = 192 * pi
Now to find the area of the triangle.
The triangle is an isosceles triangle That means two of its sides are equal. They are equal to the radius of the circle, which is 24.
the small angles are equal to
2x + 120 = 180 Subtract 120 from both sides
2x = 60 Divide by 2
x = 60/2
x = 30
The height of the triangle is derived from sin(30) = opposite / hypotenuse
sin(30) = 1/2
hypotenuse = 24
1/2 = opposite / hypotenuse
1/2 = opposite / 24 Multiply both sides by 24
1/2 * 24 = opposite
opposite = 12
The height = 12
r = 24
Area of the triangle = 1/2 * 12 * 24
Area of the triangle = 144
So the area of the shaded area = 192*pi - 144 which looks like B
