In the figure above, RSTV is a square inscribed in a circle with radiu

Question

https://gmatclub.com/forum/download/file.php?id=38605 In the figure above, RSTV is a square inscribed in a circle with radius r. In terms of r, what is the total area of the shaded regions? (A) r^2(π – 2) (B) 2r(2 – π) (C) π(r^2 – 2) (D) πr^2– 8r (E) πr^2 – 4r 2017-11-15_1035_001.png

Alexey1989x · Answer

Since RSTV is a circle the relationship between r and itrs sides would be 2^1/2 to 1
Area of squre=( 2^1/2*r)^2=2r^2
Area of circle=P*r^2
Area of shaded region=P*r^2 - 2r^2=r^2*(P-2)
Answer A

Abhishek009 · Answer

Diagonal of the square =  2r  , so area of the square =  4r^2/2  ir,  2r^2

Area of the circle =  πr^2

So, Area of the shaded region =  πr^2 - 2r^2

Or, Area of the shaded region =  r^2 ( π- 2 )  , answer will be (A)

generis · Answer

The total area of the shaded regions equals
(Area of Circle) - (Area of Square)

Area of circle =  πr^2

Area of square 
The square's diagonal = 2r

The relationship between a square's diagonal, d, and its side, s, is 
 s^2 = d , so
 s = \frac{d}{\sqrt{2}} 
 s = \frac{2r}{\sqrt{2}}

Area of square = 
 s^2 =\frac{2r}{\sqrt{2}}*
\frac{2r}{\sqrt{2}} =\frac{(4)r^2}{2}= 2r^2

Total area of shaded regions 
(Circle area) - (square area)
 (πr^2 - 2r^2) = 
 r^2(π - 2)

Answer A

cledgard · Answer

A faster approach to get the area of the square, is to treat it as a rombus. 
A = (d 1  x d 2 )/2 = 2r x 2r / 2 = 2r^2

LeoN88 · Answer

Total Area - Area of square = Shaded area Area of square: Found using this https://gmatclub.com/forum/if-a-square- ... l#p2285889 Answer= PI (r^2) - 2 (r^2) = (A) r^2(π – 2)

In the figure above, RSTV is a square inscribed in a circle with radiu

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In the figure above, RSTV is a square inscribed in a circle with radiu

Prep Toolkit

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