Question

Question #41b40

Answer 1

`16pi` sq. unit

Explanation:

As shown in the figure, a regular hexagon can be divided into 6 congruent equilateral triangles, namely, `DeltaOAB, DeltaOBC` ... etc. `O` is the center of the circles and the hexagon.
Given side length `BC=8` units,
`=>OB=8`
radius of the circumscribed circle `r_1=OB=8`

In `DeltaOMB, angleBOM=30^@`,
`=> AM=8cos30=8*(sqrt3/2)=4sqrt3`
`=>` radius of the inscribed circle `r_2=AM=4sqrt3`

`=>` area of region between the two circles
`=pi(r_1^2-r_2^2)`
`=pi(8^2-(4sqrt3)^2)`
`=16pi` sq. unit