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Vladimir79 [104]

3 years ago

6

A square is inscribed in a circle as shown. If the radius of the circle is 9, what is the area of the shaded region, rounded to

the nearest hundredth?

1 answer:

djyliett [7]3 years ago

3 0

Answer:

Area of shaded region is:

A = 92.41

Step-by-step explanation:

(As the diagram is not shown, consider the diagram attached below.)

r = 9

So

Diagonal of the square = 2r = 18

As all angles of square are of 90°

The diagonal is dividing the angles into 2 halves of 45° at point where diagonal is joining the corner.

Taking sine:

$sin\theta=\frac{perpendicular}{hypotenuse}\\perpendicular = s\\hypotenuse = 2r = 18\\\theta = 45^\circ\\Substitute:\\sin45=\frac{s}{18}\\sin45\cdot18=s\\s=12.73$

<h3>Area of Circle:</h3>

$A=\pi{r}^2\\A=\pi{9}^2\\A=254.34$

<h3>Area of Square:</h3><h3> $Area = s\cdot{s}\\Area=12.73\cdot12.73\\Area = 161.93$ </h3><h3>Area of Shaded Region:</h3>

Area of circle - Area of square

$A = 254.34-161.93\\A=92.41$

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