Answer :

mixter17

Hello!

The answer is:

The difference between the circle and the square is:

[tex]Difference=4\pi -8[/tex]

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:

[tex]side=2\sqrt{2}[/tex]

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

[tex]diagonal=side*\sqrt{2}[/tex]

So,

[tex]diagonal=2\sqrt{2}*\sqrt{2}=2*(\sqrt{2})^{2}=2*2=4units[/tex]

The area will be:

[tex]Area_{square}=side^{2}= (2\sqrt{2})^{2} =4*2=8units^{2}[/tex]

For the circle we have:

[tex]radius=\frac{4units}{2}=2units[/tex]

The area will be:

[tex]Area_{Circle}=\pi *radius^{2}=\pi *2^{2}=\pi *4=4\pi units^{2}[/tex]

[tex]Area_{Circle}=4\pi units^{2}[/tex]

Then, the difference will be:

[tex]Difference=Area_{Circle}-Area{Square}=4\pi -8[/tex]

Have a nice day!

kudzordzifrancis

ANSWER

[tex]4\pi - 8[/tex]

EXPLANATION

The diagonal of the square can be found

using Pythagoras Theorem.

[tex] {d}^{2} = {(2 \sqrt{2} )}^{2} + {(2 \sqrt{2} )}^{2} [/tex]

[tex]{d}^{2} = 4 \times 2+ 4 \times 2[/tex]

[tex]{d}^{2} = 8+ 8[/tex]

[tex]{d}^{2} = 16[/tex]

Take positive square root

[tex]d = \sqrt{16} = 4[/tex]

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

Hence r=2 units.

Area of circle is

[tex]\pi {r}^{2} =\pi \times {2}^{2} = 4\pi[/tex]

The area of the square is

[tex] {l}^{2} = {(2 \sqrt{2)} }^{2} = 4 \times 2 = 8[/tex]

The difference in area is

[tex]4\pi - 8[/tex]