Respuesta :

The area of a circle is given by the following formula:

[tex]A_C=\pi\cdot r^2[/tex]

where r is the lenght of the circle's radius.

In this case, we have a radius of 12 units, so the area will be

[tex]A_C=\pi\cdot12^2=3.14\cdot144=452.16[/tex]

We are however, asked to find the area of the shaded region, which is encased within a square. From the image we can see that the circle's radius is half the length of a side of the square. In other words, the square's sides measure 24 units.

The area of a square is given by

[tex]A_S=s^2[/tex]

where s is the lenght of the sides of the square. In this case,

[tex]A_S=24^2=576[/tex]

Now, in order to determine the area of the shaded region, we subtract the area of the circle from the area of the square:

[tex]A_R=A_S-A_C=576-452.16=123.84[/tex]

So the area of the shaded region is 123.84 square units.

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