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505-555 (Easy)|   Geometry|      
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Bunuel
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In the figure above, the area of the shaded square region is what Fri Jan 20, 2023 1:30 am
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Difficulty:

15% (low)

Question Stats:

88% (01:25) correct 12% (02:46) wrong based on 25 sessions

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In the figure above, the area of the shaded square region is what percent of the area of the square region ABCD?


A. \(16 \frac{2}{3}\) %

B. \(12 \frac{1}{2}\) %

C. \(12\) %

D. \(8 \frac{1}{2}\) %

E. \(8\) %




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In the figure above, the area of the shaded square region is what Fri Jan 20, 2023 12:07 pm
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Bunuel

In the figure above, the area of the shaded square region is what percent of the area of the square region ABCD?


A. \(16 \frac{2}{3}\) %

B. \(12 \frac{1}{2}\) %

C. \(12\) %

D. \(8 \frac{1}{2}\) %

E. \(8\) %
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Let the side of the square ABCD = 2s units

AX = s units

In \(\triangle AYX \)

  • \(\angle YAX = 45\)
  • \( \angle AXY = 45\)
  • \( \angle XYA = 90\)
  • AX = s units

Therefore using 45 - 45 - 90

\(YX =\frac{ s}{\sqrt{2}}\)

Area of square XYOZ = \(YX =(\frac{ s}{\sqrt{2}})^2 = \frac{s^2}{2}\)

Area of square ABCD= \(YX =(2s)^2 = 4s^2\)

Required Percentage = \(\frac{s^2}{2} / 4s^2 * 100 = \frac{1}{8} * 100 = 12.5 \)%

Option B
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