BTGmoderatorDC wrote:
In the figure above, the area of the shaded region is
A. \(8\sqrt{2}\)
B. \(4\sqrt{3}\)
C. \(4\sqrt{2}\)
D. \(8\sqrt{3} - 1)\)
E. \(8\sqrt{2} - 1)\)
OA
D
Source: Official Guide
Note that the two sides of the non-shades quadrilateral are 4 and each angle is 90º, thus, it is a square. Thus, the length of the diagonal = 4√2.
This makes an equilateral triangle with a side 4√2. The area of the equilateral triangle = √3/4*side^2 = √3/4*(4√2)^ = 8√3
Area of the shaded region = Area of the equilateral triangle - Area of half-square = 8√3 - (4*4)/2 = 8√3 - 8 = 8(√3 - 1)
The correct answer: [spoiler][/spoiler]
Hope this helps!
-Jay
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