Question

Please respond asap!!!

Answer 1

`4\pi - 8`

Step-by-step explanation

The diagonal of the square can be found

using Pythagoras Theorem.

`{d}^(2) = {(2 √(2) )}^(2) + {(2 √(2) )}^(2)`

`{d}^(2) = 4 * 2+ 4 * 2`

`{d}^(2) = 8+ 8`

`{d}^(2) = 16`

Take positive square root

`d = √(16) = 4`

The radius is half the diagonal because the diagonal formed the diameter of the circle.

Hence r=2 units.

Area of circle is

`\pi {r}^(2) =\pi * {2}^(2) = 4\pi`

The area of the square is

`{l}^(2) = {(2 √(2)) }^(2) = 4 * 2 = 8`

The difference in area is

`4\pi - 8`

Answer 2

Hello!

The answer is:

The difference between the circle and the square is:

`Difference=4\pi -8`

Why?

To solve the problem, we need to find the area of the circle and the area of the square, and then, subtract them.

For the square we have:

`side=2√(2)`

We can calculate the diagonal of a square using the following formula:

`diagonal=side*√(2)`

So,

`diagonal=2√(2)*√(2)=2*(√(2))^(2)=2*2=4units`

The area will be:

`Area_(square)=side^(2)= (2√(2))^(2) =4*2=8units^(2)`

For the circle we have:

`radius=(4units)/(2)=2units`

The area will be:

`Area_(Circle)=\pi *radius^(2)=\pi *2^(2)=\pi *4=4\pi units^(2)`

`Area_(Circle)=4\pi units^(2)`

Then, the difference will be:

`Difference=Area_(Circle)-Area{Square}=4\pi -8`

Have a nice day!