What is the area of the shaded region in the given circle in terms of pi and in simplest form.
a. (270pi +54radical3) m^2
b. (216 pi +54radical3) m^2
c. (216 pi + 81radical3) m^2
d. (270 pi +81radical3) m^2

D. (270 pi +81radical3) m^2

Step-by-step explanation:

In order to determine the area of the shaded region, we need to  

determine the area of the circle, the sector and the triangle  

that is a part of the sector. Do the following steps and work:

Area of the circle:

πr² = π(18)² = 324π

Area of the sector:

(60/360) (324π) = 54π

Area of the triangle:

60/2=30

1/2 (b)(h) = 1/2 (18cos30)(18) = 81√3

Area of the shaded region:

324π - 54π + 81√3 = 270π + 18√3

The answer is D. (270π + 18√3)m²