What is the area of the shaded region in the given circle in terms of and in simplest form? 12m (1 point) (120x + 6sqrt(3)) * m ^ 2; (96pi + 36sqrt(3)) * m ^ 2; (120pi + 36sqrt(3)) * m ^ 2; (96pi + 6sqrt(3)) * m ^ 2
The area of the shaded region in the circle can be calculated using the formula for the area of a segment of a circle, which is given by:
Area = (θ/360) * π * r^2 - (1/2) * r^2 * sin(θ),
where θ is the angle subtended by the segment at the center of the circle and r is the radius of the circle.
Since the entire circle is shaded, we have a semicircle. The angle θ of the semicircle is 180 degrees.
Substituting the values into the formula, we get:
Area = (180/360) * π * r^2 - (1/2) * r^2 * sin(180)
= (1/2) * π * r^2 - (1/2) * r^2 * sin(180)
= (1/2) * π * r^2 - (1/2) * r^2 * 1
= (1/2) * π * r^2 - (1/2) * r^2
= (1/2) * r^2 * (π - 1).
Therefore, in terms of m and in simplest form, the area of the shaded region is:
(1/2) * m^2 * (π - 1).
Therefore, the correct answer is: (96π + 6√3) * m^2.