Question

Find the perimeter of the shaded region. Round your answer to the nearest hundredth.

Answer 1

20.56 units.

Explanation:

Perimeter of the shaded region is the sum of all straight sides and all 4 arcs.

Perimeter of 4 straight sides
`=4* 2=8\text{ units}`

Perimeter of a arc
`=(1)/(4)* 2\pi r`

Perimeter of 4 arcs
`=4* (1)/(4)(2\pi r)=2\pi r`

Here, r is the radius. So,

`r=(6-2)/(2)=(4)/(2)=2`

Perimeter of 4 arcs
`=2(3.14)(2)=12.56`

Perimeter of the shaded region = Perimeter of all straight sides + Perimeter of all 4 arcs

`=8+12.56`

`=20.56\text{ units}`

Therefore, the perimeter of the shaded region is 20.56 units.