# Given the radius of the circle inscribing the hexagon is #r# express the shaded area in terms of #r#?

##### 2 Answers

#### Explanation:

Area

The 3 green areas in sector

One green area

The black area

Now, let the shaded area in your diagram be

Given the radius of the circle inscribing the hexagon is **r**

The area of the circle

**The area of the each of 6 equilateral triangles** having length of each side r is

**Area of each of the segment** of circle marked **X**

From the figure it is obvious that **the area of Yellow shaded region in the given figure is**