Question

Find the area of the shaded region.

Answer 1

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 :

${:\implies{\tt{A_{(Circle)} = \pi {r}^{2}}}}$

${:\implies{\tt{A_{(Circle)} = 3.14{(8)}^{2}}}}$

${:\implies{\tt{A_{(Circle)} = 3.14{(8 \times 8)}}}}$

${:\implies{\tt{A_{(Circle)} = 3.14{(64)}}}}$

${:\implies{\tt{A_{(Circle)} = 3.14 \times 64}}}$${:\implies{\tt{A_{(Circle)} = 200.96 \: {m}^{2} }}}$

Hence, the area of circle is 200.96 m².

$\begin{gathered}\end{gathered}$

Secondly, finding the area of rectangle with length and breadth by substituting the values in the formula :

${:\implies{\tt{A_{(Rectangle)} = l \times b}}}$

${:\implies{\tt{A_{(Rectangle)} = 12 \times 8}}}$

${:\implies{\tt{A_{(Rectangle)} = 96 \: {m}^{2}}}}$

Hence, the area of rectangle is 96 m².

$\begin{gathered}\end{gathered}$

Now, finding the area of shaded region by substituting the values in the formula :

${:\implies{\tt{A_{(Shaded)} = A_{(Circle)} - A_{(Rectangle)}}}}$

${:\implies{\tt{A_{(Shaded)} = 200.96 - 96}}}$

${:\implies{\tt{A_{(Shaded)} = 104.96 \: {m}^{2}}}}$

Hence, the area of shaded region is 104.96 m².

$\rule{300}{2.5}$