Question

Determine the shaded area.

9 ft
(
The shaded area is
(Round to two decimal places as needed.)

Answer 1

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 :

• radius = 9ft

To find :

• Area of circle

Solution:

We know :

`\boxed{ \rm Area \: of \: circle =\pi {r}^(2) }`

Steps :

`\dashrightarrow\sf Area \: of \: circle =\pi {r}^(2)`

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`\dashrightarrow\sf Area \: of \: circle = (22)/(7) * {9}^(2)`

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`\dashrightarrow\sf Area \: of \: circle = (22)/(7) * 9 * 9`

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`\dashrightarrow\sf Area \: of \: circle = (22)/(7) * 81`

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`\dashrightarrow\sf Area \: of \: circle = (22* 81)/(7)`

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`\dashrightarrow\sf Area \: of \: circle = (1782)/(7)`

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`\dashrightarrow\bf Area \: of \: circle =254.57 \: ft {}^(2) \\`

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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 :-

`\boxed{ \rm Diameter \: of \: circle =2 \: radius}`

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Steps:-

`\dashrightarrow\sf Diameter \: of \: circle =2 \: radius \\`

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`\dashrightarrow\sf Diameter \: of \: circle =2 * 9\\`

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`\dashrightarrow\bf Diameter \: of \: circle =18 \: ft`

We have :

• side of square = 18 ft

To find:

• Area of square

Solution:

We know :

`\boxed{ \rm Area \: of \: square= {side}^(2) }`

Steps :

`\dashrightarrow\sf Area \: of \: square= {side}^(2)`

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`\dashrightarrow\sf Area \: of \: square= {18}^(2)`

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`\dashrightarrow\sf Area \: of \: square= {18} * 18`

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`\dashrightarrow\bf Area \: of \: square= 324 \: {ft}^(2)`

Part three:

Remember the first line of answer ? :)

So let's insert here:-

`\boxed{ \text{Shaded area = area of square - area of a circle}}`

Steps :-

`\dashrightarrow\textsf{Shaded area = area of square - area of a circle} \\`

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`\dashrightarrow\textsf{Shaded area = 324 - 254.57} \\`

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`\dashrightarrow\textbf{Shaded area = 69.43 }\bf {ft}^(2) \\`