Question

What will be the area of the shaded part ?

Answer 1

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