What will be the area of the shaded part ?

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

∠acb = 8°

step-by-step explanation:

∠xba lies on the circle and is half the measure of the intercepted arc ax

hence

measure of arc ax = 2 × 42° = 84°

∠acb is outside the circle and is

∠acb = (arcab - arcax ), hence

∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°