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In the figure shown, PQRS is a square, T is the midpoint of
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21 Nov 2019, 11:35
21 Nov 2019, 11:35
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Question Stats:
71% (01:38) correct
28% (02:17) wrong based on 42 sessions
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Attachment:
#greprepclub In the figure shown.jpg [ 27.25 KiB | Viewed 5937 times ]
In the figure shown, \(PQRS\) is a square, \(T\) is the midpoint of side \(PS\), and \(U\) is the midpoint of side \(QR\). The area of the shaded region is what fraction of the area of square \( PQRS\) ?
A. \(\frac{1}{6
}\)
B. \(\frac{1}{8}\)
C. \(\frac{1}{5}\)
D. \(\frac{1}{4}\)
E. \(\frac{1}{3}\)
Kudos for the right answer and solution.
Re: In the figure shown, PQRS is a square, T is the midpoint of
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20 Apr 2020, 15:55
20 Apr 2020, 15:55
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Expert Reply
PTUR is a parallelogram so the area is x/2*x = x^2/2
the shaded portion is half of this
so it is x^2/4
Area of square x^2
(x^2/4)/x^2
=1/4
the shaded portion is half of this
so it is x^2/4
Area of square x^2
(x^2/4)/x^2
=1/4
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
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Re: In the figure shown, PQRS is a square, T is the midpoint of
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28 Jul 2020, 06:26
28 Jul 2020, 06:26
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1
Carcass wrote:
Attachment:
#greprepclub In the figure shown.jpg
In the figure shown, \(PQRS\) is a square, \(T\) is the midpoint of side \(PS\), and \(U\) is the midpoint of side \(QR\). The area of the shaded region is what fraction of the area of square \( PQRS\) ?
A. \(\frac{1}{6
}\)
B. \(\frac{1}{8}\)
C. \(\frac{1}{5}\)
D. \(\frac{1}{4}\)
E. \(\frac{1}{3}\)
Kudos for the right answer and solution.
Let's say that each side of the square has length 2
Which means its area = (2)(2) = 4
Since T and U are midpoints, we get the following measurements:
Since URPT is a parallelogram, its area = (base)(height) = (1)(2) = 2
Since the blue line divides parallelogram URPT into 2 EQUAL pieces, the area of the shaded region = 1/2 of 2, which is 1
The area of the shaded region is what fraction of the area of square PQRS?
Fraction = 1/4
Answer: D
Cheers,
Brent
