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Sub 505 (Easy)|   Geometry|      
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Bunuel
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The area of square ABCD above is 18. The shaded region is the intersec 29 Apr 2021, 01:30
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The area of square ABCD above is 18. The shaded region is the intersection of the square and a circular region centered at C. What is the area of the shaded region?

A. \(18-\frac{9}{4}*\pi\)

B. \(18-\frac{9}{2}*\pi\)

C. \(9+\frac{9}{4}*\pi\)

D. \(9+\frac{9}{2}*\pi\)

E. \(\frac{9}{2}-\frac{9}{4}*\pi\)


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B
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The area of square ABCD above is 18. The shaded region is the intersec 29 Apr 2021, 02:26
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Area of square = 18
Therefore, length of the side = \(\sqrt{18}\)

Radius of the Quarter circle = Length of the side of square = \(\sqrt{18}\)
Area of full circle = \(π*18\)
Area of Quarter circle = \(π*18/4 = π*9/2\)

Therefore, Area of shaded region = \(18 - π*9/2\)

Answer: B
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The area of square ABCD above is 18. The shaded region is the intersec 29 Apr 2021, 03:35
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The area of square ABCD is 18.
Therefore, length of the side = √18
Radius of the Quarter circle = Length of the side of square =√18
Area of full circle = Pi * Radius^2
Area of Quarter circle = Pi* \(\frac{18}{4}\)

Therefore, Area of shaded region = 18−pi∗\(\frac{9}{2}\)
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The area of square ABCD above is 18. The shaded region is the intersec 29 Apr 2021, 07:12
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IMO B

Area of the square =18
Side of the square = √18= 3√2
Hence the radius of the circular region =3√2
Area of of the quarter circle =π(3√2)^2 /4=9π/2
Hence the area of the shaded region =(18-9π/2)

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The area of square ABCD above is 18. The shaded region is the intersec 29 Apr 2021, 14:06
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Area of the shaded region = Area of square - \(\frac{1}{4}\) * area of circle

= 18- π*\(\frac{18}{4}\) = 18- \(\frac{9π}{2}\)

So, I think B. :)
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The area of square ABCD above is 18. The shaded region is the intersec 30 Apr 2021, 02:54
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Area of the shaded region = Area of square - 1414 * area of circle
Area of the square =18
Side of the square = √18= 3√2
Hence the radius of the circular region =3√2
Area of of the quarter circle =π(3√2)^2 /4=9π/2
Hence the area of the shaded region =(18-9π/2)
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The area of square ABCD above is 18. The shaded region is the intersec 05 May 2021, 01:37
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Area of the shaded region = Total Area- Unshaded portion

Total Area= Area of the square=18
Unshaded portion= Length of the Arc= Teta/360*2*pi\(\)*r

90/360*2*pi\(\)*9= 9/2*pi\(\)

Area of the shaded region= 18- 9/2*pi\(\)

Option B
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The area of square ABCD above is 18. The shaded region is the intersec 26 Nov 2022, 04:04
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