Diameter of the circle in the middle = 8 ft
Radius of the circle in the middle :
[tex] =\tt \: \frac{Diameter }{2} [/tex]
[tex] =\tt \frac{8}{2} [/tex]
[tex] =\tt 4 \: ft[/tex]
Thus, the radius of the circle in the middle = 4 ft
Area of the entire circle :
[tex] =\tt \pi {r}^{2} [/tex]
[tex] = \tt3.14 \times 4 + 6 \times 4 + 6[/tex]
[tex] = \tt3.14 \times 10 \times 10[/tex]
[tex] =\tt 3.14 \times 100[/tex]
[tex]\color{plum} = \tt314 \: ft[/tex]
Thus, the area of the entire circle = 314 ft
Area of the circle in the middle :
[tex] =\tt \pi {r}^{2} [/tex]
[tex] =\tt 3.14 \times 4 \times 4[/tex]
[tex] = \tt3.14 \times 16[/tex]
[tex]\color{plum} =\tt 50.24 \: ft[/tex]
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
[tex] =\tt 314 - 50.24[/tex]
[tex]\color{plum} =\tt 263.76 \: ft[/tex]
▪︎Therefore, the area of the shaded portion = 263.76 ft
