Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of π (no approximations).

  27π cm^2

Step-by-step explanation:

The area of a circle is given by the formula ...

  A = πr^2

So, the area of a circle with radius 6 cm is ...

  A = π(6 cm)^2 = 36π cm^2

The shaded portion of the given figure is 3/4 of a full circle of radius 6 cm, so has an area of ...

  (3/4)(36π cm^2) = 27π cm^2 . . . . shaded area

-30/48 = 0.625
-5/8 = 0.625
10/-16 = 0.625
-35/56 = 0.625

all options are correct.