Answer:
34.785 units²
Step-by-step explanation:
The area of each triangular section of the hexagon is ...
... A = (1/2)sin(60°)·8²
There are 6 such sections, so their total area (the area of the hexagon) is ...
... 6A = 6·(1/2)·sin(60°)·8² = 3sin(60°)·8² . . . . . hexagon area
The area of the circumscribing circle is ...
... A = πr² = π·8²
The shaded area is the difference between the area of the circle and the area of the hexagon:
... shaded area = π·8² -3sin(60°)·8² = 64(π -3sin(60°))
... shaded area ≈ 34.785 units²
