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# In square PQRS above, if ST = TQ and SU = RU, then the area of the sha

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
In square PQRS above, if ST = TQ and SU = RU, then the area of the sha  [#permalink]

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16 Oct 2018, 00:25
00:00

Difficulty:

15% (low)

Question Stats:

94% (00:47) correct 6% (00:37) wrong based on 20 sessions

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In square PQRS above, if ST = TQ and SU = RU, then the area of the shaded region is what fraction of the area of square region PQRS?

(A) 1/16
(B) 1/8
(C) 1/6
(D) 1/4
(E) 1/3

Attachment:

2018-10-16_1223.png [ 12.46 KiB | Viewed 243 times ]

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Re: In square PQRS above, if ST = TQ and SU = RU, then the area of the sha  [#permalink]

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16 Oct 2018, 00:30
Since SQ is the diagonal of the square PQRS. Area of triangle SRQ will be half of PQRS. Now Triangle TUR is 1/4 of the area of SRQ. Hence the triangle TUR will be 1/8 of the area of the triangle PQRS.

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Re: In square PQRS above, if ST = TQ and SU = RU, then the area of the sha  [#permalink]

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16 Oct 2018, 00:40
1
ST=TQ tells us that T is the center of the square.
SU=RU tells us that U is the midpoint of SR.

This translates to TUR being $$\frac{1}{2}$$ of TSR
TSR is $$\frac{1}{2}$$ of SQR

There can be 8 equal segments of area TUR in the square, therefore TUR is $$\frac{1}{8}$$ the area of the square.
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Re: In square PQRS above, if ST = TQ and SU = RU, then the area of the sha   [#permalink] 16 Oct 2018, 00:40
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