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 :

$=\tt \: \frac{Diameter }{2}$

$=\tt \frac{8}{2}$

$=\tt 4 \: ft$

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

Area of the entire circle :

$=\tt \pi {r}^{2}$

$= \tt3.14 \times 4 + 6 \times 4 + 6$

$= \tt3.14 \times 10 \times 10$

$=\tt 3.14 \times 100$

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

Thus, the area of the entire circle = 314 ft

Area of the circle in the middle :

$=\tt \pi {r}^{2}$

$=\tt 3.14 \times 4 \times 4$

$= \tt3.14 \times 16$

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

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