Answer:
Area of the shaded region is 104.96 m².
Step-by-step explanation:
Firstly, finding the area of circle with radius 8 cm by substituting the values in the formula :
[tex]{:\implies{\tt{A_{(Circle)} = \pi {r}^{2}}}}[/tex]
[tex]{:\implies{\tt{A_{(Circle)} = 3.14{(8)}^{2}}}}[/tex]
[tex]{:\implies{\tt{A_{(Circle)} = 3.14{(8 \times 8)}}}}[/tex]
[tex]{:\implies{\tt{A_{(Circle)} = 3.14{(64)}}}}[/tex]
[tex]{:\implies{\tt{A_{(Circle)} = 3.14 \times 64}}}[/tex][tex]{:\implies{\tt{A_{(Circle)} = 200.96 \: {m}^{2} }}}[/tex]
Hence, the area of circle is 200.96 m².
[tex]\begin{gathered}\end{gathered}[/tex]
Secondly, finding the area of rectangle with length and breadth by substituting the values in the formula :
[tex]{:\implies{\tt{A_{(Rectangle)} = l \times b}}}[/tex]
[tex]{:\implies{\tt{A_{(Rectangle)} = 12 \times 8}}}[/tex]
[tex]{:\implies{\tt{A_{(Rectangle)} = 96 \: {m}^{2}}}}[/tex]
Hence, the area of rectangle is 96 m².
[tex]\begin{gathered}\end{gathered}[/tex]
Now, finding the area of shaded region by substituting the values in the formula :
[tex]{:\implies{\tt{A_{(Shaded)} = A_{(Circle)} - A_{(Rectangle)}}}}[/tex]
[tex]{:\implies{\tt{A_{(Shaded)} = 200.96 - 96}}}[/tex]
[tex]{:\implies{\tt{A_{(Shaded)} = 104.96 \: {m}^{2}}}}[/tex]
Hence, the area of shaded region is 104.96 m².
[tex]\rule{300}{2.5}[/tex]
