In square PQRS above, QR = 1, RU = US, and PT = TS. What is the area

Question

https://gmatclub.com/forum/download/file.php?id=37977 In square PQRS above, QR = 1, RU = US, and PT = TS. What is the area of the quadrilateral PRUT? (A) 1/8 (B) 1/4 (C) 3/8 (D) 5/8 (E) 2/3 2017-10-11_1127.png

Alexey1989x · Answer

Area of PQRS = 1 ==> Areas of PRS=1/2
We know that iaw similarity properties:
Area of PRS/Area of TUS = RS^2/US^2= 1^2/0,5^2=1/0,25
Area of TUS = 1/8, therefore Area of PRTU = Area of PRS - Area of TUS = 1/2-1/8=3/8
 
Answer C.

souvonik2k · Answer

Side QR=1
Area of square PQRS = 1^2 =1
Area of triangle PRS = 1/2 of PQRS = 1/2
Area of triangle UTS = 1/2 * ST * SU = 1/2 *1/2 * 1/2 = 1/8
Area of quadrilateral PRUT = Area of triangle PRS - Area of triangle UTS =1/2 - 1/8 = 3/8
Answer C.

JeffTargetTestPrep · Answer

The area of square QRPS is 1 x 1 = 1.

The area of triangle QRP is 1/2.

The area of triangle TUS is 1/2 x 1/2 x 1/2 = 1/8.

Thus, the area of the quadrilateral PRUT is 1 - (1/2 + 1/8) = 1 - (4/8 + 1/8) = 3/8.

Answer: C

kaleem765 · Answer

Area of PRUT = Area of PQRS - Area of UST - Area of PQR

Area of PQRS = 1*1 = 1

Since QR = PQ = 1 so Area of PQR = 1/2 * 1 * 1 = 1/2

Since RU = US = ST = PT = 1/2 so Area of UST = 1/2 * 1/2 * 1/2 = 1/8

So the area of PRUT = 1 -1/2 -1/8 = 3/8

ANSWER: C

atulindia · Answer

If we divide square into triangles it would be 8 triangles of equal area
in shaded portion there are 3 triangles so ea of Quad is 3/8
Answer is C

generis · Answer

(Area_{square}) - (Area_{2triangles}) = (Area_{quad})

Square side length = 1
Top triangle legs' length = 1
Bottom triangle legs' length* =  \frac{1}{2}

Area of square:  s^2 = 1^2 = 1 
Area of top triangle:  \frac{s^2}{2}=\frac{1}{2}  
Area of bottom triangle:  \frac{s^2}{2} 
=\frac{(\frac{1}{4})}{2} = \frac{1}{8}

Both triangles' area:
 \frac{1}{2} + \frac{1}{8} = \frac{5}{8}

Quadrilateral area:  1 - \frac{5}{8}=\frac{3}{8}

Answer C

* The segments that constitute the legs of this right triangle are both  \frac{1}{2}  the length of the side of the square because they are half of a bisected side.
Square side RS is bisected; we are given that RU = US. Square side PS is similarly bisected.

In square PQRS above, QR = 1, RU = US, and PT = TS. What is the area

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GMAT Problem Solving (PS) Questions

In square PQRS above, QR = 1, RU = US, and PT = TS. What is the area

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