Shaded area = area of square - area of a circle.
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For this we have to find area of both square and circle which is visible in the picture.
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Part one :
In this part we'll find area of circle.
Given :
To find :
Solution:
We know :
[tex] \boxed{ \rm Area \: of \: circle =\pi {r}^{2} }[/tex]
Steps :
[tex] \dashrightarrow\sf Area \: of \: circle =\pi {r}^{2}[/tex]
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[tex] \dashrightarrow\sf Area \: of \: circle = \dfrac{22}{7} \times {9}^{2} [/tex]
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[tex] \dashrightarrow\sf Area \: of \: circle = \dfrac{22}{7} \times 9 \times 9[/tex]
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[tex] \dashrightarrow\sf Area \: of \: circle = \dfrac{22}{7} \times 81[/tex]
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[tex] \dashrightarrow\sf Area \: of \: circle = \dfrac{22\times 81}{7}[/tex]
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[tex] \dashrightarrow\sf Area \: of \: circle = \dfrac{1782}{7}[/tex]
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[tex] \dashrightarrow\bf Area \: of \: circle =254.57 \: ft {}^{2} \\ [/tex]
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Part 2
As it's visible diameter of circle = side of square.
So we have to find diameter of circle.
We know :-
[tex] \boxed{ \rm Diameter \: of \: circle =2 \: radius}[/tex]
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Steps:-
[tex] \dashrightarrow\sf Diameter \: of \: circle =2 \: radius \\ [/tex]
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[tex] \dashrightarrow\sf Diameter \: of \: circle =2 \times 9\\ [/tex]
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[tex] \dashrightarrow\bf Diameter \: of \: circle =18 \: ft[/tex]
We have :
To find:
Solution:
We know :
[tex] \boxed{ \rm Area \: of \: square= {side}^{2} }[/tex]
Steps :
[tex] \dashrightarrow\sf Area \: of \: square= {side}^{2}[/tex]
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[tex] \dashrightarrow\sf Area \: of \: square= {18}^{2}[/tex]
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[tex] \dashrightarrow\sf Area \: of \: square= {18} \times 18[/tex]
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[tex] \dashrightarrow\bf Area \: of \: square= 324 \: {ft}^{2} [/tex]
Part three:
Remember the first line of answer ? :)
So let's insert here:-
[tex] \boxed{ \text{Shaded area = area of square - area of a circle}}[/tex]
Steps :-
[tex] \dashrightarrow\textsf{Shaded area = area of square - area of a circle} \\ [/tex]
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[tex] \dashrightarrow\textsf{Shaded area = 324 - 254.57} \\ [/tex]
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[tex] \dashrightarrow\textbf{Shaded area = 69.43 }\bf {ft}^{2} \\ [/tex]
