Answer:
Area of the shaded region 45.76 cm².
Step-by-step explanation:
Firstly, finding the area of rectangle by substituting the values in the formula :
[tex]{\longrightarrow{\pmb{\sf{A_{(Rectangle)} = l \times b}}}}[/tex]
- → A = Area
- → l = length
- → b = breadth
[tex]\begin{gathered} \qquad{\longrightarrow{\sf{A_{(Rectangle)} = l \times b}}}\\\\\qquad{\longrightarrow{\sf{A_{(Rectangle)} = 12\times 8}}}\\\\\qquad{\longrightarrow{\sf{A_{(Rectangle)} = 96}}}\\\\\qquad{\star{\boxed{\sf{\pink{A_{(Rectangle)} = 96 \: {cm}^{2}}}}}} \end{gathered}[/tex]
Hence, the area of rectangle is 96 cm².
[tex]\rule{200}2[/tex]
Secondly, finding the area of circle by substituting the values in the formula :
[tex]{\longrightarrow{\pmb{\sf{A_{(Circle)} = \pi{r}^{2}}}}}[/tex]
- → A = Area
- → π = 3.14
- → r = radius
[tex]\begin{gathered} \qquad{\longrightarrow{\sf{A_{(Circle)} = \pi{r}^{2}}}} \\ \\ \qquad{\longrightarrow{\sf{A_{(Circle)} = 3.14{(4)}^{2}}}} \\ \\ \qquad{\longrightarrow{\sf{A_{(Circle)} = 3.14{(4\times 4)}}}} \\ \\ \qquad{\longrightarrow{\sf{A_{(Circle)} = 3.14(16)}}} \\ \\ \qquad{\longrightarrow{\sf{A_{(Circle)} = 3.14 \times 16}}} \\ \\ \qquad{\longrightarrow{\sf{A_{(Circle)} \approx 50.24}}} \\ \\ \qquad{\star{\boxed{\sf{\purple{A_{(Circle)} \approx 50.24 \: {cm}^{2}}}}}} \end{gathered}[/tex]
Hence, the area of circle is 50.24 cm².
[tex]\rule{200}2[/tex]
Now, finding the area of shaded region by substituting the values in the formula :
[tex]\longrightarrow{\pmb{\sf{A_{(Shaded)} = A_{(Rectangle)} - A_{(Circle)}}}}[/tex]
- → A = Area
- → Rectangle
- → Circle
[tex]\begin{gathered}{\quad{\longrightarrow{\sf{A_{(Shaded)} = A_{(Rectangle)} - A_{(Circle)}}}}}\\\\{\quad{\longrightarrow{\sf{A_{(Shaded)} = 96 - 50.24}}}}\\\\{\quad{\longrightarrow{\sf{A_{(Shaded)} \approx 45.76}}}}\\\\{\quad{\star{\boxed{\sf{\red{A_{(Shaded)} \approx 45.76 \: {cm}^{2}}}}}}} \end{gathered}[/tex]
Hence, the area of shaded region is 45.76 cm².
[tex]\rule{300}{2.5}[/tex]
