Question

Determine the shaded area.

Answer 1

Shaded area = area of square - area of a circle.

For this we have to find area of both square and circle which is visible in the picture.

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 :

$\dashrightarrow\sf Area \: of \: circle =\pi {r}^{2}$

$\dashrightarrow\sf Area \: of \: circle = \dfrac{22}{7} \times {9}^{2}$

$\dashrightarrow\sf Area \: of \: circle = \dfrac{22}{7} \times 9 \times 9$

$\dashrightarrow\sf Area \: of \: circle = \dfrac{22}{7} \times 81$

$\dashrightarrow\sf Area \: of \: circle = \dfrac{22\times 81}{7}$

$\dashrightarrow\sf Area \: of \: circle = \dfrac{1782}{7}$

$\dashrightarrow\bf Area \: of \: circle =254.57 \: ft {}^{2}$

Part 2

As it's visible diameter of circle = side of square.

So we have to find diameter of circle.

We know :-

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

Steps:-

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

$\dashrightarrow\sf Diameter \: of \: circle =2 \times 9$

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

We have :

• side of square = 18 ft

To find:

• Area of square

Solution:

We know :

$\boxed{ \rm Area \: of \: square= {side}^{2} }$

Steps :

$\dashrightarrow\sf Area \: of \: square= {side}^{2}$

$\dashrightarrow\sf Area \: of \: square= {18}^{2}$

$\dashrightarrow\sf Area \: of \: square= {18} \times 18$

$\dashrightarrow\bf Area \: of \: square= 324 \: {ft}^{2}$

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 :-

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

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

$\dashrightarrow\textbf{Shaded area = 69.43 }\bf {ft}^{2}$