A is the center of the circle, and the length of AB is . The blue shad

Question

areashade_q2.png A is the center of the circle, and the length of AB is 4\sqrt{2} . The blue shaded region is a square. What is the area of the shaded region? A. 4(4 - π) B. 4(8 - π) C. 8(2 - π) D. 8(8 - π) E. 16(4 - π) Kudos for a correct solution .

hsbinfy · Answer

correct choice is E

side of square =2r

4sqt2=r *sqt2

r=4

so we can calculate the area of square and circle and minus
which boils down to option E for the correct answer

bhatiamanu05 · Answer

consider radius of circle = r
so side of square = 2r

r^2+r^2 = {4sqrt(2)}^2
2r^2 = 32
r^2 = 16

so area of circle = pi*r^2 => pi*16
area of square = 4*r^2 = 4*16
so area of shaded region == area of square - area of cirlce == 16(4-pi)

ngie · Answer

Since AB is half the diagonal of the square, the diagonal is  8\sqrt{2} , which is  \sqrt{2}  the side of the square. The side of the square is then  \frac{8\sqrt{2}}{\sqrt{2}}=8 .

The area of the square is then  8^2=64 .

The side of the square equals twice the radium of the circle. Therefore, the area of the circle is  \pi\cdot4^2=16\pi

The shaded area is  64-16\pi=16(4-\pi)

The correct answer is E

peachfuzz · Answer

The line segment AB forms a 45 45 90 triangle with a hypotenuse of  4\sqrt{2} 
As a result both a side of the square and the radius is 4.
8^2 - (4^2)π
16(4 - π)

Answer: E

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION: areashade_explanation.png

PareshGmat · Answer

There is a direct relation between area of inscribed circle & area of square

Area of circle = Area of square * \frac{\pi}{4}

Diagonal of square  = 2 * 4\sqrt{2} = 8\sqrt{2}

Side of square  = \sqrt{\frac{(8\sqrt{2})^2}{2}} = 8

Area of square  = 8^2 = 64

Area of circle  = 64 * \frac{\pi}{4} = 16\pi

Area of shaded region  = 64 - 16\pi = 16(4-\pi)

CrackverbalGMAT · Answer

Hi All,
Area of the shaded region = Area of the square – area of the circle.
Since line segment AB forms the 45-45-90 triangle with square.
It gives side of the square as 8. And radius of the circle as 4.
Area of the shaded region = 64 – 16pi.
 = 16(4-Pi).
You can also approach this question using POE. 
 the shaded region should be slightly less than 1/4th of the area of the square. Since area of the square is 64. We are looking some answer close to 16.
Let pi = 3.1
A. 4(4 - π) this is less than 4 eliminate.
B. 4(8 - π) this is more than 16 eliminate.
C. 8(2 - π) this is negative eliminate.
D. 8(8 - π) this is more than 16 eliminate.
E. 16(4 - π) this is very close to 16. So answer is E.
POE is just in case if you don’t know how to solve.

testcracker · Answer

okay

since the length of AB is 4√2, the diagonal of the square is 8√2, and thus each side of the square measures 8 and radius of the circle measures 4

now the shaded area = 64 - pi 4^2 = 16(4-pi) = E the answer

thanks

bumpbot · Answer

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A is the center of the circle, and the length of AB is . The blue shad

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A is the center of the circle, and the length of AB is . The blue shad

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