Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. The square upper A upper B upper C upper D is shown with a circle upper O inscribed inside of the square. The side upper A upper B is labeled 8. The area of the square outside of the circle is shaded. Find the area of the shaded region to the nearest tenth.

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MrRoyal MrRoyal · Answer 1 · 2021-09-20T18:37:16+02:00

The area of a shape is the amount of space it can occupy.

The area of the shaded region is 13.7 square units

Given

[tex]AB = 8[/tex]

First, calculate the area of the square

[tex]Area = Length^2[/tex]

So, we have:

[tex]Area = AB^2[/tex]

[tex]Area = 8^2[/tex]

[tex]Area = 64[/tex]

The length of the square represents the diameter of the circle.

So, the radius (r) of the circle is:

[tex]r = \frac{AB}{2}[/tex]

[tex]r = \frac{8}{2}[/tex]

[tex]r = 4[/tex]

The area of the circle is:

[tex]Area = \pi r^2[/tex]

[tex]Area = 3.143 \times 4^2[/tex]

[tex]Area = 50.3[/tex]

The shaded region is the area of the circle subtracted from the area of the square.

So, we have:

[tex]Shaded = 64-50.3[/tex]

[tex]Shaded = 13.7[/tex]

Hence, the shaded region is 13.7 square units