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In the figure above, the area of the shaded square region is
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28 Dec 2020, 11:34
28 Dec 2020, 11:34
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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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GRE In the figure above, the area of the shaded square region.jpg [ 20.27 KiB | Viewed 2051 times ]
Re: In the figure above, the area of the shaded square region is
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31 Dec 2020, 20:04
31 Dec 2020, 20:04
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A diagonal divides the square into 2 parts.
Here two diagonals are dividing the square in 4 parts.
Each part is divided into 4 triangles. The shaded region has 2 triangles.
This is, 50% of the part.
Therefore, the area of shaded region is 50% of 25% of the square => 50/100 x 25/100 --> 1/2 x 1/4 --> 1/8.
= 0.125 => 12.5% => 12 1/2%. Hence the correct answer is option B.
Here two diagonals are dividing the square in 4 parts.
Each part is divided into 4 triangles. The shaded region has 2 triangles.
This is, 50% of the part.
Therefore, the area of shaded region is 50% of 25% of the square => 50/100 x 25/100 --> 1/2 x 1/4 --> 1/8.
= 0.125 => 12.5% => 12 1/2%. Hence the correct answer is option B.
Re: In the figure above, the area of the shaded square region is
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03 Jan 2021, 02:57
03 Jan 2021, 02:57
1
Let us consider the side of the big square as a
The area of the big square would then be \(a^2\)
Any diagonal cuts through the square in equal halves. With 2 diagonals the square is split in 4 equal sizes.
The area of the big triangle consisting the shaded square is \(\frac{1}{4} \) \(a^2\)
If you take any diagonal of the shaded square its length would be \(\frac{1}{2}\) a
The shaded square can be divided into two equal triangle of 45-45-90
The length of such a triangle is \(x:x:x\sqrt{2}\)
Therefore, \(x\sqrt{2}\) = \(\frac{1}{2}\) a
From this we can calculate a side of the shaded square as \(1/2\sqrt{2}\)*\(a\)
Area of the shaded square would be \(\frac{1}{2}\sqrt{2} * a \)* \(1/2\sqrt{2} * a\) = \(\frac{1}{8}\) * \(a^2
\)
Hence, this enables us to calculate the percentage as:
\(\frac{1}{8}\) \(a^2\) / \(a^2\) * 100
\(a^2\) cancels out giving \(\frac{100}{8}\) = 12.5 %
The area of the big square would then be \(a^2\)
Any diagonal cuts through the square in equal halves. With 2 diagonals the square is split in 4 equal sizes.
The area of the big triangle consisting the shaded square is \(\frac{1}{4} \) \(a^2\)
If you take any diagonal of the shaded square its length would be \(\frac{1}{2}\) a
The shaded square can be divided into two equal triangle of 45-45-90
The length of such a triangle is \(x:x:x\sqrt{2}\)
Therefore, \(x\sqrt{2}\) = \(\frac{1}{2}\) a
From this we can calculate a side of the shaded square as \(1/2\sqrt{2}\)*\(a\)
Area of the shaded square would be \(\frac{1}{2}\sqrt{2} * a \)* \(1/2\sqrt{2} * a\) = \(\frac{1}{8}\) * \(a^2
\)
Hence, this enables us to calculate the percentage as:
\(\frac{1}{8}\) \(a^2\) / \(a^2\) * 100
\(a^2\) cancels out giving \(\frac{100}{8}\) = 12.5 %
