What is the approximate area of the shaded region?
2 answers:
Answer:
At = 21.5 cm2
Step-by-step explanation:
At = Asqr - Acircle
At = A1 - A2
A1 = 10^2 = 100
A2 = Pi*(5)^2 = 78.5
At = 100 - 78.5
At = 21.5 cm2
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For this case we have that by definition:
The area of a circle is: ![A_ {c} = \pi * r ^ 2](https://tex.z-dn.net/?f=A_%20%7Bc%7D%20%3D%20%5Cpi%20%2A%20r%20%5E%202)
Where r is the radius of the circle.
The area of a square is: ![A_ {s} = l ^ 2](https://tex.z-dn.net/?f=A_%20%7Bs%7D%20%3D%20l%20%5E%202)
Where l is the side of the square.
The area of the shaded region will be:
![A_ {sr} = A {s} -A_ {c}](https://tex.z-dn.net/?f=A_%20%7Bsr%7D%20%3D%20A%20%7Bs%7D%20-A_%20%7Bc%7D)
So:
![A_ {s} = 10 * 10\\A_ {s} = 100 \ cm ^ 2](https://tex.z-dn.net/?f=A_%20%7Bs%7D%20%3D%2010%20%2A%2010%5C%5CA_%20%7Bs%7D%20%3D%20100%20%5C%20cm%20%5E%202)
On the other hand:
![A_ {c} = \pi * (\frac {10} {2}) ^ 2\\A_ {c} = \pi * 25\\A_ {c} = 78.5375cm ^ 2](https://tex.z-dn.net/?f=A_%20%7Bc%7D%20%3D%20%5Cpi%20%2A%20%28%5Cfrac%20%7B10%7D%20%7B2%7D%29%20%5E%202%5C%5CA_%20%7Bc%7D%20%3D%20%5Cpi%20%2A%2025%5C%5CA_%20%7Bc%7D%20%3D%2078.5375cm%20%5E%202)
Finally:
![A_ {sr} = 100-78.5375\\A_ {sr} = 21.4625](https://tex.z-dn.net/?f=A_%20%7Bsr%7D%20%3D%20100-78.5375%5C%5CA_%20%7Bsr%7D%20%3D%2021.4625)
Rounding out, we have that the area of the shaded region is 21.5 square centimeters.
Answer:
Option D
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