Question

4. Find the area of the
shaded region.

Answer 1

Diameter of the circle in the middle = 8 ft

Radius of the circle in the middle :

`=\tt \: (Diameter )/(2)`

`=\tt (8)/(2)`

`=\tt 4 \: ft`

Thus, the radius of the circle in the middle = 4 ft

Area of the entire circle :

`=\tt \pi {r}^(2)`

`= \tt3.14 * 4 + 6 * 4 + 6`

`= \tt3.14 * 10 * 10`

`=\tt 3.14 * 100`

`\color{plum} = \tt314 \: ft`

Thus, the area of the entire circle = 314 ft

Area of the circle in the middle :

`=\tt \pi {r}^(2)`

`=\tt 3.14 * 4 * 4`

`= \tt3.14 * 16`

`\color{plum} =\tt 50.24 \: ft`

Thus, the area of the circle in the middle = 50.24 ft

Area of the shaded portion :

= Total area of the figure - Area of the circle in middle

`=\tt 314 - 50.24`

`\color{plum} =\tt 263.76 \: ft`

▪︎Therefore, the area of the shaded portion = 263.76 ft